{"title":"New Results on One Modulo N-Difference Mean Graphs","authors":"Pon Jeyanthi, Meganathan Selvi, Damodaran Ramya","doi":"10.4236/ojdm.2023.134010","DOIUrl":"https://doi.org/10.4236/ojdm.2023.134010","url":null,"abstract":"A graph G is said to be one modulo N-difference mean graph if there is an injective function f from the vertex set of G to the set , where N is the natural number and q is the number of edges of G and f induces a bijection from the edge set of G to given by and the function f is called a one modulo N-difference mean labeling of G. In this paper, we show that the graphs such as arbitrary union of paths, , ladder, slanting ladder, diamond snake, quadrilateral snake, alternately quadrilateral snake, , , , , friendship graph and admit one modulo N-difference mean labeling.","PeriodicalId":222803,"journal":{"name":"Open journal of Discrete Mathematics","volume":"147 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135107338","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":"Cycle Multiplicity of Total Graph of Complete Bipartite Graph","authors":"Ganghua Xie, Yinkui Li","doi":"10.4236/ojdm.2023.134009","DOIUrl":"https://doi.org/10.4236/ojdm.2023.134009","url":null,"abstract":"Cycle multiplicity of a graph G is the maximum number of edge disjoint cycles in G. In this paper, we determine the cycle multiplicity of and then obtain the formula of cycle multiplicity of total graph of complete bipartite graph, this generalizes the result for, which is given by M.M. Akbar Ali in [1].","PeriodicalId":222803,"journal":{"name":"Open journal of Discrete Mathematics","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135798558","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}