Pub Date : 2021-06-14DOI: 10.1080/23799927.2021.1934900
Ke Wang, Jiannan Zhou, Dong He, Qin Tong
For bipartite graphs , the bipartite Ramsey number is the least positive integer p so that any coloring of the edges of with k colors will result in a copy of in the ith color for some i. In this paper, we investigate the appearance of simpler monochromatic graphs such as paths under a 3-colouring of the edges of a bipartite graph. we obtain the exact value of , and for , and for by a new method of proof.
{"title":"Note on the three-coloured bipartite Ramsey numbers for paths","authors":"Ke Wang, Jiannan Zhou, Dong He, Qin Tong","doi":"10.1080/23799927.2021.1934900","DOIUrl":"https://doi.org/10.1080/23799927.2021.1934900","url":null,"abstract":"For bipartite graphs , the bipartite Ramsey number is the least positive integer p so that any coloring of the edges of with k colors will result in a copy of in the ith color for some i. In this paper, we investigate the appearance of simpler monochromatic graphs such as paths under a 3-colouring of the edges of a bipartite graph. we obtain the exact value of , and for , and for by a new method of proof.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"54 1","pages":"189 - 193"},"PeriodicalIF":0.8,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77622663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-14DOI: 10.1080/23799927.2021.1931455
B. Fine, M. Kreuzer, G. Rosenberger
Group theory, specifically the combinatorial group theory of finitely presented groups,has been utilized effectively in cryptology. Several new public key cryptosystems have been developed and this has ushered a new area in cryptography called group based cryptography. Braid groups have been suggested as possible platforms and this has led to what is called braid group cryptography. This has also had a profound effect on theoretical group theory as techniques have been found to analyse these group-based cryptosystems.The basic idea is that a finitely presented group can be described by a finite amount of data.This provides techniques to enormously compress and hide information. This suggests that we have only barely scraped the surface of using finitely presented groups for data control, security and storage. For example, we describe a far-reaching extension for controlling access to files which could be relevant in medical records.
{"title":"Further potential applications of group theory in information security","authors":"B. Fine, M. Kreuzer, G. Rosenberger","doi":"10.1080/23799927.2021.1931455","DOIUrl":"https://doi.org/10.1080/23799927.2021.1931455","url":null,"abstract":"Group theory, specifically the combinatorial group theory of finitely presented groups,has been utilized effectively in cryptology. Several new public key cryptosystems have been developed and this has ushered a new area in cryptography called group based cryptography. Braid groups have been suggested as possible platforms and this has led to what is called braid group cryptography. This has also had a profound effect on theoretical group theory as techniques have been found to analyse these group-based cryptosystems.The basic idea is that a finitely presented group can be described by a finite amount of data.This provides techniques to enormously compress and hide information. This suggests that we have only barely scraped the surface of using finitely presented groups for data control, security and storage. For example, we describe a far-reaching extension for controlling access to files which could be relevant in medical records.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"124 1","pages":"375 - 380"},"PeriodicalIF":0.8,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23799927.2021.1931455","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72534204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-30DOI: 10.1080/23799927.2021.1930176
Nir Drucker, S. Gueron, Dusan Kostic, Edoardo Persichetti
The QC-MDPC code-based KEM BIKE is one of the Round-3 candidates of the NIST PQC standardization project. Its Round-2 specification document described variants claiming to have IND-CCA security. The security proof used the Fujisaki–Okamoto transformation and a decoder targeting a Decoding Failure Rate (DFR) of (for Level-1 security). However, several aspects needed to be amended in order for the IND-CCA proof to hold. The main issue is that using a decoder with DFR of does not necessarily imply that the underlying PKE is δ-correct with , as required. In this paper, we handle the necessary aspects to ensure the security claim is correct. In particular, we close the gap in the proof by defining the notion of message-agnostic PKE. We show that the PKEs underlying the BIKE versions are message-agnostic. This implies that BIKE with a decoder that has a sufficiently low DFR is also an IND-CCA KEM.
{"title":"On the applicability of the Fujisaki–Okamoto transformation to the BIKE KEM","authors":"Nir Drucker, S. Gueron, Dusan Kostic, Edoardo Persichetti","doi":"10.1080/23799927.2021.1930176","DOIUrl":"https://doi.org/10.1080/23799927.2021.1930176","url":null,"abstract":"The QC-MDPC code-based KEM BIKE is one of the Round-3 candidates of the NIST PQC standardization project. Its Round-2 specification document described variants claiming to have IND-CCA security. The security proof used the Fujisaki–Okamoto transformation and a decoder targeting a Decoding Failure Rate (DFR) of (for Level-1 security). However, several aspects needed to be amended in order for the IND-CCA proof to hold. The main issue is that using a decoder with DFR of does not necessarily imply that the underlying PKE is δ-correct with , as required. In this paper, we handle the necessary aspects to ensure the security claim is correct. In particular, we close the gap in the proof by defining the notion of message-agnostic PKE. We show that the PKEs underlying the BIKE versions are message-agnostic. This implies that BIKE with a decoder that has a sufficiently low DFR is also an IND-CCA KEM.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"23 1","pages":"364 - 374"},"PeriodicalIF":0.8,"publicationDate":"2021-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86476283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-01DOI: 10.1080/23799927.2021.1905715
Chunhua Cao, Haiyan Liu, Di Yang
Since the union and the production of two d-codes may not be d-codes, in this paper, we aim to give some necessary and sufficient conditions for them.
由于两个d码的并集和产生可能不是d码，本文给出了它们存在的充分必要条件。
{"title":"Some properties of d-codes","authors":"Chunhua Cao, Haiyan Liu, Di Yang","doi":"10.1080/23799927.2021.1905715","DOIUrl":"https://doi.org/10.1080/23799927.2021.1905715","url":null,"abstract":"Since the union and the production of two d-codes may not be d-codes, in this paper, we aim to give some necessary and sufficient conditions for them.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"8 1","pages":"167 - 177"},"PeriodicalIF":0.8,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85265483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-04DOI: 10.1080/23799927.2021.1884605
R. Azarderakhsh, Jean-François Biasse, R. Khatib, Brandon Langenberg, Benjamin Pring
In this paper we study a strategy for adapting the “Tiny Claw” Grover-based attack of Biasse and Pring (A framework for reducing the overhead of the quantum oracle for use with Grover's algorithm with applications to cryptanalysis of SIKE, J. Math. Cryptol. 15 (2019), pp. 143–156) for attacking SIKE and abstract it under a realistic model of classical memory-access costs. Our results allow us to retain the almost quadratic reduction in the overheads involved with the implementing the quantum oracle in this cost model and demonstrate how the cost of the parallel version of this attack scales in a manner superior to that of a naive use of Grover’s algorithm. In order to investigate the utility of the Tiny Claw approach, we perform a quantum resource estimation of the classical and quantum resources required to attack various SIKE instances with Tiny Claw when when we are limited to hardware, finding interesting price-points.
在本文中，我们研究了一种策略，以适应Biasse和Pring基于Grover的“Tiny Claw”攻击(一种用于减少与Grover算法一起使用的量子预言器开销的框架，用于SIKE, J. Math的密码分析)。Cryptol. 15 (2019)， pp. 143-156)攻击SIKE，并将其抽象在经典内存访问成本的现实模型下。我们的结果使我们能够保留在这个成本模型中实现量子预言器所涉及的开销的几乎二次减少，并演示了这种攻击的并行版本的成本如何以优于单纯使用Grover算法的方式进行扩展。为了研究Tiny Claw方法的效用，当我们限于硬件时，我们对使用Tiny Claw攻击各种SIKE实例所需的经典和量子资源进行了量子资源估计，找到了有趣的价格点。
{"title":"Parallelism strategies for the tuneable golden-claw finding problem","authors":"R. Azarderakhsh, Jean-François Biasse, R. Khatib, Brandon Langenberg, Benjamin Pring","doi":"10.1080/23799927.2021.1884605","DOIUrl":"https://doi.org/10.1080/23799927.2021.1884605","url":null,"abstract":"In this paper we study a strategy for adapting the “Tiny Claw” Grover-based attack of Biasse and Pring (A framework for reducing the overhead of the quantum oracle for use with Grover's algorithm with applications to cryptanalysis of SIKE, J. Math. Cryptol. 15 (2019), pp. 143–156) for attacking SIKE and abstract it under a realistic model of classical memory-access costs. Our results allow us to retain the almost quadratic reduction in the overheads involved with the implementing the quantum oracle in this cost model and demonstrate how the cost of the parallel version of this attack scales in a manner superior to that of a naive use of Grover’s algorithm. In order to investigate the utility of the Tiny Claw approach, we perform a quantum resource estimation of the classical and quantum resources required to attack various SIKE instances with Tiny Claw when when we are limited to hardware, finding interesting price-points.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"119 1","pages":"337 - 363"},"PeriodicalIF":0.8,"publicationDate":"2021-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77321565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-08DOI: 10.1080/23799927.2021.2006314
Delaram Kahrobaei, A. Tortora, M. Tota
In Kahrobaei et al. [Multilinear cryptography using nilpotent groups, Proceedings of Elementary Theory of Groups and Group Rings, and Related Topics conference. Conference held at Fairfield University and at the Graduate Center, CUNY, New York, NY, USA, November 1–2, 2018, De Gruyter, 2020, pp. 127–133] we generalized the definition of a multilinear map to arbitrary groups and introduced two multiparty key-exchange protocols using nilpotent groups. In this paper we have a closer look at the protocols and will address some incorrect cryptanalysis which has been proposed in Roman'kov [Discrete logarithm for nilpotent groups and cryptanalysis of polylinear cryptographic system, Prikl. Diskretn. Mat. Suppl. (12), (2019), pp. 154–160].
Kahrobaei et al.[利用幂零群的多线性密码学]，群与群环的基本理论论文集，及相关主题会议。在费尔菲尔德大学和研究生中心举行的会议，纽约，NY, USA, 11月1-2日，2018,De Gruyter, 2020, pp. 127-133]我们将多线性映射的定义推广到任意群，并引入了两个使用幂零群的多方密钥交换协议。在本文中，我们仔细研究了这些协议，并将解决在Roman'kov[幂零群的离散对数]和多线性密码系统的密码分析中提出的一些错误的密码分析。Diskretn。垫,增刊。(12)， (2019)， pp. 154-160]。
{"title":"A closer look at the multilinear cryptography using nilpotent groups","authors":"Delaram Kahrobaei, A. Tortora, M. Tota","doi":"10.1080/23799927.2021.2006314","DOIUrl":"https://doi.org/10.1080/23799927.2021.2006314","url":null,"abstract":"In Kahrobaei et al. [Multilinear cryptography using nilpotent groups, Proceedings of Elementary Theory of Groups and Group Rings, and Related Topics conference. Conference held at Fairfield University and at the Graduate Center, CUNY, New York, NY, USA, November 1–2, 2018, De Gruyter, 2020, pp. 127–133] we generalized the definition of a multilinear map to arbitrary groups and introduced two multiparty key-exchange protocols using nilpotent groups. In this paper we have a closer look at the protocols and will address some incorrect cryptanalysis which has been proposed in Roman'kov [Discrete logarithm for nilpotent groups and cryptanalysis of polylinear cryptographic system, Prikl. Diskretn. Mat. Suppl. (12), (2019), pp. 154–160].","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"9 1","pages":"63 - 67"},"PeriodicalIF":0.8,"publicationDate":"2021-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91086013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-28DOI: 10.1080/23799927.2021.1873192
Suvradip Chakraborty, Y. S. Rao, C. Rangan
ABSTRACT Attribute-Based Authenticated Key Exchange (ABAKE) protocols allow two or more users to establish a shared key and achieve mutual authentication over an insecure network, while providing fine-grained access control over transmitted data. The existing ABAKE protocols are very inefficient, requiring a large number (polynomial in the size of the access policies) of pairing and exponentiation operations. This presents a major hindrance in the real-world deployment of these protocols. In this work, we present a construction of ABAKE protocol where the number of pairing operations is constant (to be precise only 7) and the number of exponentiation operations is linear to the number of clauses in the disjunctive normal form representing the general access policies. To this end, we construct an Attribute-Based Signcryption (ABSC) scheme with constant number of pairings, and use it as the main building block in our ABAKE construction. This also gives the first construction of ABSC schemes with constant number of pairings for general purpose access policies in the standard model. Another important and desirable feature of our ABAKE construction is that it is round-optimal, i.e. it is a single round protocol. We analyse the security of our ABAKE construction in the Attribute-Based extended Canetti-Krawzyck (ABeCK) model, and prove its security assuming the hardness of a variant of the Bilinear Diffie-Hellman Exponent problem in the random oracle model.
{"title":"Efficient single round attribute-based authenticated key exchange protocol","authors":"Suvradip Chakraborty, Y. S. Rao, C. Rangan","doi":"10.1080/23799927.2021.1873192","DOIUrl":"https://doi.org/10.1080/23799927.2021.1873192","url":null,"abstract":"ABSTRACT Attribute-Based Authenticated Key Exchange (ABAKE) protocols allow two or more users to establish a shared key and achieve mutual authentication over an insecure network, while providing fine-grained access control over transmitted data. The existing ABAKE protocols are very inefficient, requiring a large number (polynomial in the size of the access policies) of pairing and exponentiation operations. This presents a major hindrance in the real-world deployment of these protocols. In this work, we present a construction of ABAKE protocol where the number of pairing operations is constant (to be precise only 7) and the number of exponentiation operations is linear to the number of clauses in the disjunctive normal form representing the general access policies. To this end, we construct an Attribute-Based Signcryption (ABSC) scheme with constant number of pairings, and use it as the main building block in our ABAKE construction. This also gives the first construction of ABSC schemes with constant number of pairings for general purpose access policies in the standard model. Another important and desirable feature of our ABAKE construction is that it is round-optimal, i.e. it is a single round protocol. We analyse the security of our ABAKE construction in the Attribute-Based extended Canetti-Krawzyck (ABeCK) model, and prove its security assuming the hardness of a variant of the Bilinear Diffie-Hellman Exponent problem in the random oracle model.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"1 1","pages":"313 - 336"},"PeriodicalIF":0.8,"publicationDate":"2021-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76605242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-20DOI: 10.1080/23799927.2021.1872707
Hongyan Cai, Qiang Sun
ABSTRACT DP-colouring (also known as correspondence colouring), introduced by Dvořák and Postle, is a generalization of list colouring. Many results on list-colouring of graphs, especially of planar graphs, have been extended to the setting of DP-colouring. Recently, Pongpat and Kittikorn [P. Sittitrai and K. Nakprasit, Suffficient conditions on planar graphs to have a relaxed DP-3-colourability, Graphs and Combinatorics 35 (2019), pp. 837–845.] introduced DP- -colouring to generalize -colouring and -choosability. They proved that every planar graph G without -cycles is DP- -colourable. In this note, we show the following results:(1) Every planar graph G without -cycles is DP- -colourable; (2) Every planar graph G without -cycles is DP- -colourable; (3) Every planar graph G without -cycles is DP- -colourable.
{"title":"A note on improper DP-colouring of planar graphs","authors":"Hongyan Cai, Qiang Sun","doi":"10.1080/23799927.2021.1872707","DOIUrl":"https://doi.org/10.1080/23799927.2021.1872707","url":null,"abstract":"ABSTRACT DP-colouring (also known as correspondence colouring), introduced by Dvořák and Postle, is a generalization of list colouring. Many results on list-colouring of graphs, especially of planar graphs, have been extended to the setting of DP-colouring. Recently, Pongpat and Kittikorn [P. Sittitrai and K. Nakprasit, Suffficient conditions on planar graphs to have a relaxed DP-3-colourability, Graphs and Combinatorics 35 (2019), pp. 837–845.] introduced DP- -colouring to generalize -colouring and -choosability. They proved that every planar graph G without -cycles is DP- -colourable. In this note, we show the following results:(1) Every planar graph G without -cycles is DP- -colourable; (2) Every planar graph G without -cycles is DP- -colourable; (3) Every planar graph G without -cycles is DP- -colourable.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"1 1","pages":"159 - 166"},"PeriodicalIF":0.8,"publicationDate":"2021-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80301319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-16DOI: 10.1080/23799927.2021.1973567
Kijung Kim
Let be a graph. A subset D of V is a restrained dominating set if every vertex in is adjacent to a vertex in D and to a vertex in . The restrained domination number, denoted by , is the smallest cardinality of a restrained dominating set of G. A function is a restrained Italian dominating function on G if (i) for each vertex for which , it holds that , (ii) the subgraph induced by has no isolated vertices. The restrained Italian domination number, denoted by , is the minimum weight taken over all restrained Italian dominating functions of G. It is known that for any graph G. In this paper, we characterize the trees T for which , and we also characterize the trees T for which .
{"title":"Restrained Italian domination in trees","authors":"Kijung Kim","doi":"10.1080/23799927.2021.1973567","DOIUrl":"https://doi.org/10.1080/23799927.2021.1973567","url":null,"abstract":"Let be a graph. A subset D of V is a restrained dominating set if every vertex in is adjacent to a vertex in D and to a vertex in . The restrained domination number, denoted by , is the smallest cardinality of a restrained dominating set of G. A function is a restrained Italian dominating function on G if (i) for each vertex for which , it holds that , (ii) the subgraph induced by has no isolated vertices. The restrained Italian domination number, denoted by , is the minimum weight taken over all restrained Italian dominating functions of G. It is known that for any graph G. In this paper, we characterize the trees T for which , and we also characterize the trees T for which .","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"8 1","pages":"236 - 242"},"PeriodicalIF":0.8,"publicationDate":"2021-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76046478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-15DOI: 10.1080/23799927.2020.1871418
S. Raja, I. Rajasingh, Antony Xavier
ABSTRACT The minimum induced H-packing k-partition number is denoted by . The induced H-packing k-partition number denoted by is defined as where the minimum is taken over all H-packings of G. In this paper, we obtain the induced -packing k-partition number for trees, slim trees, split graphs, complete bipartite graphs, grids and circulant graphs. We also deal with networks having perfect -packing where is a claw on four vertices. We prove that an induced -packing k-partition problem is NP-Complete. Further we prove that the induced -packing k-partition number of is 2 for all hypercube networks with perfect -packing and prove that for all locally twisted cubes with perfect -packing.
{"title":"Induced H-packing k-partition of graphs","authors":"S. Raja, I. Rajasingh, Antony Xavier","doi":"10.1080/23799927.2020.1871418","DOIUrl":"https://doi.org/10.1080/23799927.2020.1871418","url":null,"abstract":"ABSTRACT The minimum induced H-packing k-partition number is denoted by . The induced H-packing k-partition number denoted by is defined as where the minimum is taken over all H-packings of G. In this paper, we obtain the induced -packing k-partition number for trees, slim trees, split graphs, complete bipartite graphs, grids and circulant graphs. We also deal with networks having perfect -packing where is a claw on four vertices. We prove that an induced -packing k-partition problem is NP-Complete. Further we prove that the induced -packing k-partition number of is 2 for all hypercube networks with perfect -packing and prove that for all locally twisted cubes with perfect -packing.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":"6 1","pages":"143 - 158"},"PeriodicalIF":0.8,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87888717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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