the chromatic number of a graph g, denoted by χ(g), is the minimum number of colors such that g can be colored with these colors in such a way that no two adjacent vertices have the same color. a clique in a graph is a set of mutually adjacent vertices. the maximum size of a clique in a graph g is called the clique number of g. the turán graph tn(k) is a complete k-partite graph whose partition...

The chromatic number of a graph G, denoted by χ(G), is the minimum number of colors such that G can be colored with these colors in such a way that no two adjacent vertices have the same color. A clique in a graph is a set of mutually adjacent vertices. The maximum size of a clique in a graph G is called the clique number of G. The Turán graph Tn(k) is a complete k-partite graph whose partition...

we give a new recursive method to compute the number of cliques and cycles of a graph. this method is related, respectively to the number of disjoint cliques in the complement graph and to the sum of permanent function over all principal minors of the adjacency matrix of the graph. in particular, let $g$ be a graph and let $overline {g}$ be its complement, then given the chromatic polynomial of...

This paper studies the maximum-clique independence problem and some variations of clique transversal such as {k}-clique, maximum-clique, minus clique, signed k-fold problems from algorithmic aspects for k-trees, suns, planar graphs, doubly chordal perfect total split line dually graphs. We give equations to compute numbers show that {k}-clique is polynomial-time solvable graphs whose equal thei...

‎the annihilator graph $ag(r)$ of a commutative ring $r$ is a simple undirected graph with the vertex set $z(r)^*$ and two distinct vertices are adjacent if and only if $ann(x) cup ann(y)$ $ neq $ $ann(xy)$‎. ‎in this paper we give the sufficient condition for a graph $ag(r)$ to be complete‎. ‎we characterize rings for which $ag(r)$ is a regular graph‎, ‎we show that $gamma (ag(r))in {1,2}$ and...