{"title":"ON CONVEX SUBGRAPH POLYNOMIALS AND SOME OF ITS IMPORTANT VALUES","authors":"Ladznar S. Laja","doi":"10.17654/0974165824004","DOIUrl":"https://doi.org/10.17654/0974165824004","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":"31 8","pages":""},"PeriodicalIF":0.1,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139382901","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":"CONVEX SUBGRAPH POLYNOMIALS OF DEGREE 3 OR 4, ROOTED AND CO-NORMAL PRODUCTS OF GRAPHS","authors":"Ladznar S. Laja","doi":"10.17654/0974165824002","DOIUrl":"https://doi.org/10.17654/0974165824002","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":"15 3","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138585344","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":"POST-QUANTUM CRYPTOGRAPHY FOR HEALTHCARE: A NUMBER THEORY BASED TWO-FACTOR MUTUAL AUTHENTICATION AND KEY EXCHANGE PROTOCOL OVER LATTICES FOR TMIS","authors":"Sidoine Djimnaibeye, Aminata Ngom, Djiby Sow","doi":"10.17654/0974165824001","DOIUrl":"https://doi.org/10.17654/0974165824001","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":"15 3","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138604273","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":"HUB ZAGREB ENERGY OF GRAPHS","authors":"V. Mathad, Anand","doi":"10.17654/0974165823068","DOIUrl":"https://doi.org/10.17654/0974165823068","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":"7 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139225816","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}
Aziz B. Tapeing, Ladznar S. Laja, Javier Hassan, Hounam B. Copel
{"title":"TOTALLY SEGREGATED POLYNOMIAL OF GRAPHS","authors":"Aziz B. Tapeing, Ladznar S. Laja, Javier Hassan, Hounam B. Copel","doi":"10.17654/0974165823067","DOIUrl":"https://doi.org/10.17654/0974165823067","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":"37 3","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139250631","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":"THE MOORE-PENROSE INVERSE OF THE RECTANGULAR FIBONACCI MATRIX AND APPLICATIONS TO THE CRYPTOLOGY","authors":"Süleyman Aydınyüz, Mustafa Aşcı","doi":"10.17654/0974165823066","DOIUrl":"https://doi.org/10.17654/0974165823066","url":null,"abstract":"","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":" 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135242080","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}
John Russel D. Evangelista, Hounam B. Copel, Mercedita A. Langamin, Nurijam Hanna M. Mohammad, Sisteta U. Kamdon, Alcyn R. Bakkang
This paper presents some results on the geodetic polynomials of some graphs, in particular, the geodetic polynomials of $n$-Sunlet and Triangular Snake $TS_n$ graphs. Received: August 18, 2023;Accepted: October 9, 2023
{"title":"GEODETIC POLYNOMIALS OF n-SUNLET AND TRIANGULAR SNAKE TS_n GRAPHS","authors":"John Russel D. Evangelista, Hounam B. Copel, Mercedita A. Langamin, Nurijam Hanna M. Mohammad, Sisteta U. Kamdon, Alcyn R. Bakkang","doi":"10.17654/0974165823064","DOIUrl":"https://doi.org/10.17654/0974165823064","url":null,"abstract":"This paper presents some results on the geodetic polynomials of some graphs, in particular, the geodetic polynomials of $n$-Sunlet and Triangular Snake $TS_n$ graphs. Received: August 18, 2023;Accepted: October 9, 2023","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":"80 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135934354","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}
Alcyn R. Bakkang, Regimar A. Rasid, Rosalio G. Artes
Let $G$ be a simple connected graph. Then an $i$-subset of $V(G)$ is a subset of $V(G)$ of cardinality $i$. An $i$-clique is an $i$-subset which induces a complete subgraph of $G$. The clique neighborhood polynomial of $G$ is given by $c n(G ; x, y)=sum_{j=0}^{n-i} sum_{i=1}^{omega(G)} c_{i j}(G) x^i y^j$, where $c_{i j}(G)$ is the number of $i$-cliques in $G$ with neighborhood cardinality equal to $j$ and $omega(G)$ is the cardinality of a maximum clique in $G$, called the clique number of $G$. In this paper, we obtain the clique neighborhood polynomials of the special graphs such as the complete graph, complete bipartite graph and complete $q$-partite graph using combinatorial approach. Received: September 14, 2023Accepted: October 9, 2023
{"title":"COMBINATORIAL APPROACH IN COUNTING THE NEIGHBORS OF CLIQUES IN A GRAPH","authors":"Alcyn R. Bakkang, Regimar A. Rasid, Rosalio G. Artes","doi":"10.17654/0974165823063","DOIUrl":"https://doi.org/10.17654/0974165823063","url":null,"abstract":"Let $G$ be a simple connected graph. Then an $i$-subset of $V(G)$ is a subset of $V(G)$ of cardinality $i$. An $i$-clique is an $i$-subset which induces a complete subgraph of $G$. The clique neighborhood polynomial of $G$ is given by $c n(G ; x, y)=sum_{j=0}^{n-i} sum_{i=1}^{omega(G)} c_{i j}(G) x^i y^j$, where $c_{i j}(G)$ is the number of $i$-cliques in $G$ with neighborhood cardinality equal to $j$ and $omega(G)$ is the cardinality of a maximum clique in $G$, called the clique number of $G$. In this paper, we obtain the clique neighborhood polynomials of the special graphs such as the complete graph, complete bipartite graph and complete $q$-partite graph using combinatorial approach. Received: September 14, 2023Accepted: October 9, 2023","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":"9 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135510795","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}
Aldison M. Asdain, Bayah J. Amiruddin, Regimar A. Rasid, Jeffrey Imer C. Salim, Rosalio G. Artes Jr.
A biclique in a graph $G$ is a subset of $V(G)$ which induces a complete bipartite subgraph of $G$. It is said to be balanced if it has equivalent independent vertex partitions. In this paper, we introduce a graph polynomial which represents the number of balanced bicliques of $G$ of all possible orders with corresponding common neighborhood systems and establish some results on some special graphs. Received: September 25, 2023Revised: October 10, 2023Accepted: November 1, 2023
{"title":"POLYNOMIAL REPRESENTATIONS OF A BALANCED BICLIQUE COMMON NEIGHBORHOOD SYSTEM OF GRAPHS","authors":"Aldison M. Asdain, Bayah J. Amiruddin, Regimar A. Rasid, Jeffrey Imer C. Salim, Rosalio G. Artes Jr.","doi":"10.17654/0974165823065","DOIUrl":"https://doi.org/10.17654/0974165823065","url":null,"abstract":"A biclique in a graph $G$ is a subset of $V(G)$ which induces a complete bipartite subgraph of $G$. It is said to be balanced if it has equivalent independent vertex partitions. In this paper, we introduce a graph polynomial which represents the number of balanced bicliques of $G$ of all possible orders with corresponding common neighborhood systems and establish some results on some special graphs. Received: September 25, 2023Revised: October 10, 2023Accepted: November 1, 2023","PeriodicalId":40868,"journal":{"name":"Advances and Applications in Discrete Mathematics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135647971","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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