{"title":"RESTRAINED CRITICAL AND ABUNDANT SIGNED GRAPHS","authors":"A. J. Mathias, V. Sangeetha, M. Acharya","doi":"10.17654/0974165823018","DOIUrl":"https://doi.org/10.17654/0974165823018","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43955403","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}
{"title":"OBSERVER SYNTHESIS FOR 2-D DISCRETE-TIME VARYING DELAY SYSTEMS: F-M MODEL","authors":"C. El-Kasri, M. Alfidi, A. Boua","doi":"10.17654/0974165823017","DOIUrl":"https://doi.org/10.17654/0974165823017","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45662374","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}
{"title":"EQUITABLE RESOLVING DOMINATING SETS IN GRAPHS","authors":"S. Vaidya, J. B. Kelaiya","doi":"10.17654/0974165823016","DOIUrl":"https://doi.org/10.17654/0974165823016","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2023-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43209093","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}
{"title":"NEW TOPOLOGIES ON A GRAPH","authors":"M. Alqahtani","doi":"10.17654/0974165823013","DOIUrl":"https://doi.org/10.17654/0974165823013","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2023-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42161575","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}
A connected graph G is totally segregated if every pair of adjacent vertices has distinct degrees. In this article, the class of graphs called co-segregated graphs which are complements of totally segregated graphs is discussed. The maximum size of connected totally segregated graph is found by finding minimum size of a large class of co-segregated graphs. We provide an algorithm to find minimum size of co-segregated graph. A construction of co-segregated graph of order n with minimum size is also described.
{"title":"ON CO-SEGREGATED GRAPHS","authors":"T. F. Jorry","doi":"10.17654/0974165823011","DOIUrl":"https://doi.org/10.17654/0974165823011","url":null,"abstract":"A connected graph G is totally segregated if every pair of adjacent vertices has distinct degrees. In this article, the class of graphs called co-segregated graphs which are complements of totally segregated graphs is discussed. The maximum size of connected totally segregated graph is found by finding minimum size of a large class of co-segregated graphs. We provide an algorithm to find minimum size of co-segregated graph. A construction of co-segregated graph of order n with minimum size is also described.","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2023-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42223312","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}
Rosalio G. Artes, N. H. M. Mohammad, Amy A. Laja, Nur-Hariza M. Hassan
Let G be a simple connected graph. An i-subset of V(G) is a subset of V(G) of cardinality i. An induced i-star of G is a star in G induced by an i-subset of V(G). The star polynomial representation of G is the generating function of the sequence of the number of induced i-stars in G. In this paper, we establish the star polynomials of some special graphs such as the star graph, spider graph, complete bipartite graph, and the complete q-partite graph.
{"title":"FROM GRAPHS TO POLYNOMIAL RINGS: STAR POLYNOMIAL REPRESENTATION OF GRAPHS","authors":"Rosalio G. Artes, N. H. M. Mohammad, Amy A. Laja, Nur-Hariza M. Hassan","doi":"10.17654/0974165823012","DOIUrl":"https://doi.org/10.17654/0974165823012","url":null,"abstract":"Let G be a simple connected graph. An i-subset of V(G) is a subset of V(G) of cardinality i. An induced i-star of G is a star in G induced by an i-subset of V(G). The star polynomial representation of G is the generating function of the sequence of the number of induced i-stars in G. In this paper, we establish the star polynomials of some special graphs such as the star graph, spider graph, complete bipartite graph, and the complete q-partite graph.","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2023-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49027152","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}
The total domination integrity of a simple connected graph G with no isolated vertices is denoted by TDI(G) and defined as TDI(G)=min { left | S right |+m(G-S) : S subseteq V(G) }, where S is a total dominating set of G and m(G - S) is the order of a maximum connected component of G - S. It is a new measure of vulnerability of a graph. This work is aimed to discuss total domination integrity of wheel, gear, helm, closed helm, flower graph, web graph, sunflower graph and web graph without center.
无孤立顶点的简单连通图G的总控制完整性用TDI(G)表示，定义为TDI(G)=min{左| S右|+m(G-S): S subseteq V(G)}，其中S为G的总控制集，m(G-S)为G-S的最大连通分量的阶数，是一种新的图的脆弱性度量。本研究旨在探讨轮、齿轮、舵、闭舵、花图、网图、向日葵图和无中心网图的总体控制完整性。
{"title":"TOTAL DOMINATION INTEGRITY OF WHEEL RELATED GRAPHS","authors":"N. H. Shah, P. L. Vihol","doi":"10.17654/0974165823009","DOIUrl":"https://doi.org/10.17654/0974165823009","url":null,"abstract":"The total domination integrity of a simple connected graph G with no isolated vertices is denoted by TDI(G) and defined as TDI(G)=min { left | S right |+m(G-S) : S subseteq V(G) }, where S is a total dominating set of G and m(G - S) is the order of a maximum connected component of G - S. It is a new measure of vulnerability of a graph. This work is aimed to discuss total domination integrity of wheel, gear, helm, closed helm, flower graph, web graph, sunflower graph and web graph without center.","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48067781","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}
Rosalio G. Artes, Al-Jayson U. Abubakar, Sisteta U. Kamdon
{"title":"POLYNOMIAL REPRESENTATIONS OF THE BICLIQUE NEIGHBORHOOD OF GRAPHS","authors":"Rosalio G. Artes, Al-Jayson U. Abubakar, Sisteta U. Kamdon","doi":"10.17654/0974165823010","DOIUrl":"https://doi.org/10.17654/0974165823010","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46579738","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}
{"title":"ANALYSIS OF BENEFITS OF INTEGRATING THE OPPOSITION BASED LEARNING TECHNIQUE INTO NON-DOMINATED SORTING GENETIC ALGORITHM III","authors":"Shilpi Jain, Kamlesh Kumar Dubey","doi":"10.17654/0974165823007","DOIUrl":"https://doi.org/10.17654/0974165823007","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46502469","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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