The (upper) clique number of a graph , denoted , is the number of vertices in a maximum clique of . Equivalently, it is the size of a largest clique or maximal clique of . The clique number of a graph is equal to the largest exponent in the graph's clique polynomial. The lower...
clique number of a graphLet G be a non-abelian group. The non-commuting graph $mathcal{A}_G$ of G is defined as the graph whose vertex set is the non-central elements of G and two vertices are joint if and only if they do not commute. In a finite simple graph u0393, the ...
AbstractFor each natural number n, denote by G(n) the set of all numbers c such that there exists a graph with exactly c cliques (i.e., complete subgraphs) and n vertices. We prove the asymptotic estimate |G(n)| = 0(2n· n−2/5...
CLIQUE NUMBERS OF PALEY GRAPHS The clique number of the Paley graph G(q), where q, is a prime power with q 1 (mod 4) is known to be Jq, when q, is a square. When q, is a non-square the ... Cohen,D Stephen - 《Quaestiones Mathematicae》 被引量: 35发表: 1988年 ...
The strong chromatic index of $G$ is equal to the chromatic number of the square of the line graph of $G$. The chromatic number of the square of the line graph of $G$ is greater than or equal to the clique number of the square of the line graph of $G$, denoted by $\omega(L...
GraphTheory CliqueNumber compute clique number of graph MaximumClique find maximum clique in graph Calling Sequence Parameters Options Description Examples References Compatibility Calling Sequence CliqueNumber( G ) CliqueNumber( G , opt ) MaximumClique(
In a finite simple graph Γ , the clique number of Γ is denoted by ω (Γ) . In this paper we show that if G is a finite group with ω (Γ (G)) < 13 , then G is solvable. As an application, we characterize all non-solvable groups G with ω (Γ...
They constructed a graph with chromatic number 32 and with an adjacency matrix of rank 29. It was proved by Kotlov and Lovász, [6], that the number of vertices in a twin free graph (a graph with no two vertices with the same set of neighbors) is O((2)rk(G)), where rk(G) is...
We study the zero-divisor graph Gamma(Z(p)n(alpha)) where p is a prime number, Zpn. is the set of integers modulo p(n), and Z(p)n (alpha) = {a + bx : a,b is an element of Z(p)n and X-2 = 0}. We find the clique number of Gamma(Z(p)n (alpha)) and the ...
Let G=(V,E) be a graph. A clique-transversal setD is a subset of vertices of G such that D meets all cliques of G, where a clique is defined as a complete subgraph maximal under inclusion and having at least two vertices. The clique-transversal number, denoted by τC(G), of G ...