The ( k , r ) -fan is the graph consisting of copies complete K which intersect in a single vertex, and denoted by F . Erd?s et al. (1995) [14] determined maximum number edges an n -vertex that does not contain 3 as subgraph. Furthermore, Chen (2003) [5] proved analogous result on for general case ? In this paper, we show sufficiently large graphs order no copy attain spectral radius are also e...

Abstract We focus on the automatic detection of communities in large networks, a challenging problem many disciplines (such as sociology, biology, and computer science). Humans tend to associate form families, villages, nations. Similarly, elements real-world networks naturally highly connected groups. A popular model represent such structures is clique, that is, set fully interconnected nodes....

‎in this paper‎, ‎we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is cohen-macaulay‎. ‎it is proved that if there exists a cover of an $r$-partite cohen-macaulay graph by disjoint cliques of size $r$‎, ‎then such a cover is unique‎.