Pub Date : 2022-09-26DOI: 10.1142/s1793830922501658
F. Kacı
{"title":"On disjoint maximum and maximal independent sets in graphs and inverse independence number","authors":"F. Kacı","doi":"10.1142/s1793830922501658","DOIUrl":"https://doi.org/10.1142/s1793830922501658","url":null,"abstract":"","PeriodicalId":342835,"journal":{"name":"Discret. Math. Algorithms Appl.","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133027964","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 : 2022-09-26DOI: 10.1142/s1793830922501464
Debashis Ghosh
Several reasonably cyclotomic sequences are constructed by cyclotomic classes having good pseudo-randomness property. In this paper, we derive the linear complexity of an extended binary cyclotomic sequences of order [Formula: see text] over finite field having period [Formula: see text]. Our result shows that these sequences have higher linear complexity, which can resist linear attack.
{"title":"An extension of binary cyclotomic sequences having order 2lt","authors":"Debashis Ghosh","doi":"10.1142/s1793830922501464","DOIUrl":"https://doi.org/10.1142/s1793830922501464","url":null,"abstract":"Several reasonably cyclotomic sequences are constructed by cyclotomic classes having good pseudo-randomness property. In this paper, we derive the linear complexity of an extended binary cyclotomic sequences of order [Formula: see text] over finite field having period [Formula: see text]. Our result shows that these sequences have higher linear complexity, which can resist linear attack.","PeriodicalId":342835,"journal":{"name":"Discret. Math. Algorithms Appl.","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117124753","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 : 2022-09-26DOI: 10.1142/s1793830922501671
Kaushik Chakraborty, S. Sardar, K. Shum
{"title":"On regularity and intra regularity of the components of a Morita context of monoids","authors":"Kaushik Chakraborty, S. Sardar, K. Shum","doi":"10.1142/s1793830922501671","DOIUrl":"https://doi.org/10.1142/s1793830922501671","url":null,"abstract":"","PeriodicalId":342835,"journal":{"name":"Discret. Math. Algorithms Appl.","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133439510","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 : 2022-09-23DOI: 10.1142/s1793830922501440
Wilma Laveena D' Souza, V. Chaitra, M. Kumara
For a graph [Formula: see text], a double Roman dominating function (DRDF) is a function [Formula: see text] such that each vertex [Formula: see text] with [Formula: see text] is adjacent to at least two vertices labeled [Formula: see text] or one vertex labeled [Formula: see text] and each vertex [Formula: see text] with [Formula: see text] is adjacent to at least one vertex [Formula: see text] with [Formula: see text]. The weight of [Formula: see text] is the sum of all labelings [Formula: see text] and is denoted by [Formula: see text]. If [Formula: see text] is a DRDF on [Formula: see text] with minimum weight [Formula: see text], then its inverse double Roman dominating function (IDRDF) [Formula: see text] is a DRDF on [Formula: see text], such that [Formula: see text], where [Formula: see text]. The inverse double Roman domination number (IDRDN) of [Formula: see text], denoted by [Formula: see text] is the minimum weight of such a function. We introduce this new type of inverse dominating function, obtain some bounds for the IDRDN of [Formula: see text]. We characterize the graphs having [Formula: see text] and the highest. We also present an approach for constructing graphs with the desired IDRDN.
对于一个图[公式:见文]，双罗马支配函数(DRDF)是这样一个函数[公式:见文]，使得每个顶点[公式:见文]与至少两个标记为[公式:见文]的顶点[公式:见文]或一个标记为[公式:见文]的顶点[公式:见文]相邻，并且每个顶点[公式:见文]与[公式:见文]至少相邻一个顶点[公式:见文]。[公式:见文]的权重是所有标签[公式:见文]的和，用[公式:见文]表示。如果[Formula: see text]是[Formula: see text]上具有最小权值的DRDF [Formula: see text]，那么它的逆双罗马支配函数(IDRDF) [Formula: see text]是[Formula: see text]上的DRDF，使得[Formula: see text]，其中[Formula: see text]。[Formula: see text]的逆双罗马支配数(IDRDN)，用[Formula: see text]表示为该函数的最小权值。我们引入了这类新的逆控制函数，得到了[公式:见文]的IDRDN的一些界。我们用[公式:见文本]和最高来描述图形。我们还提出了一种用期望的IDRDN构造图的方法。
{"title":"Inverse double Roman domination in graphs","authors":"Wilma Laveena D' Souza, V. Chaitra, M. Kumara","doi":"10.1142/s1793830922501440","DOIUrl":"https://doi.org/10.1142/s1793830922501440","url":null,"abstract":"For a graph [Formula: see text], a double Roman dominating function (DRDF) is a function [Formula: see text] such that each vertex [Formula: see text] with [Formula: see text] is adjacent to at least two vertices labeled [Formula: see text] or one vertex labeled [Formula: see text] and each vertex [Formula: see text] with [Formula: see text] is adjacent to at least one vertex [Formula: see text] with [Formula: see text]. The weight of [Formula: see text] is the sum of all labelings [Formula: see text] and is denoted by [Formula: see text]. If [Formula: see text] is a DRDF on [Formula: see text] with minimum weight [Formula: see text], then its inverse double Roman dominating function (IDRDF) [Formula: see text] is a DRDF on [Formula: see text], such that [Formula: see text], where [Formula: see text]. The inverse double Roman domination number (IDRDN) of [Formula: see text], denoted by [Formula: see text] is the minimum weight of such a function. We introduce this new type of inverse dominating function, obtain some bounds for the IDRDN of [Formula: see text]. We characterize the graphs having [Formula: see text] and the highest. We also present an approach for constructing graphs with the desired IDRDN.","PeriodicalId":342835,"journal":{"name":"Discret. Math. Algorithms Appl.","volume":"121 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127006768","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 : 2022-09-23DOI: 10.1142/s1793830922501452
T. Abualrub, P. Seneviratne
In this paper, we use a novel approach to describe generator polynomials of quasi-cyclic (QC) and generalized QC (GQC) codes over finite fields. Our study of QC- and GQC-codes will be general and not only restricted to one-generator codes. We prove that generator polynomials of QC-codes and GQC-codes are unique. Further, we use our results to obtain an expression for the dimensions of QC-codes and GQC-codes. As an application of our construction of these codes, we obtain many optimal linear codes over finite fields [Formula: see text] and [Formula: see text].
{"title":"Quasi-cyclic and generalized quasi-cyclic codes and uniqueness of their generators","authors":"T. Abualrub, P. Seneviratne","doi":"10.1142/s1793830922501452","DOIUrl":"https://doi.org/10.1142/s1793830922501452","url":null,"abstract":"In this paper, we use a novel approach to describe generator polynomials of quasi-cyclic (QC) and generalized QC (GQC) codes over finite fields. Our study of QC- and GQC-codes will be general and not only restricted to one-generator codes. We prove that generator polynomials of QC-codes and GQC-codes are unique. Further, we use our results to obtain an expression for the dimensions of QC-codes and GQC-codes. As an application of our construction of these codes, we obtain many optimal linear codes over finite fields [Formula: see text] and [Formula: see text].","PeriodicalId":342835,"journal":{"name":"Discret. Math. Algorithms Appl.","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123736893","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 : 2022-09-21DOI: 10.1142/s1793830922501488
A. I. Kristiana, I. Mursyidah, D. Dafik, R. Adawiyah, R. Alfarisi
Let [Formula: see text] be a simple graph and connected. A function [Formula: see text] is called vertex irregular [Formula: see text]-labeling and [Formula: see text] where [Formula: see text] The function of [Formula: see text] is called local irregular vertex coloring if every [Formula: see text] and [Formula: see text] vertex irregular labeling}. The local irregular chromatic number is denoted by [Formula: see text] In this paper, we study local irregular vertex coloring of [Formula: see text], and [Formula: see text]
{"title":"Local irregular vertex coloring of comb product by path graph and star graph","authors":"A. I. Kristiana, I. Mursyidah, D. Dafik, R. Adawiyah, R. Alfarisi","doi":"10.1142/s1793830922501488","DOIUrl":"https://doi.org/10.1142/s1793830922501488","url":null,"abstract":"Let [Formula: see text] be a simple graph and connected. A function [Formula: see text] is called vertex irregular [Formula: see text]-labeling and [Formula: see text] where [Formula: see text] The function of [Formula: see text] is called local irregular vertex coloring if every [Formula: see text] and [Formula: see text] vertex irregular labeling}. The local irregular chromatic number is denoted by [Formula: see text] In this paper, we study local irregular vertex coloring of [Formula: see text], and [Formula: see text]","PeriodicalId":342835,"journal":{"name":"Discret. Math. Algorithms Appl.","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116391110","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 : 2022-08-31DOI: 10.1142/s1793830922501543
Kannika Khompurngson, S. Sompong
{"title":"On matrix sequences represented by negative indices Pell and Pell-Lucas number with the decoding of Lucas blocking error correcting codes","authors":"Kannika Khompurngson, S. Sompong","doi":"10.1142/s1793830922501543","DOIUrl":"https://doi.org/10.1142/s1793830922501543","url":null,"abstract":"","PeriodicalId":342835,"journal":{"name":"Discret. Math. Algorithms Appl.","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128341977","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 : 2022-08-31DOI: 10.1142/s1793830922501555
M. R. Raja, J. Kok, T. A. Mangam, S. Naduvath
{"title":"Cyclic property of iterative eccentrication of a graph","authors":"M. R. Raja, J. Kok, T. A. Mangam, S. Naduvath","doi":"10.1142/s1793830922501555","DOIUrl":"https://doi.org/10.1142/s1793830922501555","url":null,"abstract":"","PeriodicalId":342835,"journal":{"name":"Discret. Math. Algorithms Appl.","volume":"134 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124371212","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 : 2022-08-24DOI: 10.1142/s179383092250152x
S. Lal, V. K. Bhat
{"title":"On the dominant local metric dimension of some planar graphs","authors":"S. Lal, V. K. Bhat","doi":"10.1142/s179383092250152x","DOIUrl":"https://doi.org/10.1142/s179383092250152x","url":null,"abstract":"","PeriodicalId":342835,"journal":{"name":"Discret. Math. Algorithms Appl.","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133014909","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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