Add to ORKGTo any finite group $G$, we may associate a graph whose vertices are the elements of $G$ and where two distinct vertices $x$ and $y$ are adjacent if and only if the order of the subgroup $\langle x, y\rangle$ is divisible by at least 3 distinct primes. We prove that the subgraph of this graph induced by the non-isolated vertices is connected and has diameter at most 5
Given a 2-generated finite group G, the non-generating graph of G has as vertices the elements of G ...
Given a non-abelian finite group $G$, let $pi(G)$ denote the set of prime divisors of the order of $...
Let G be a finite group. The prime graph of G is the graph whose vertex set is the prime divisors of...
In this paper we consider a prime graph of finite groups. In particular, we expect finite groups wit...
Let $G$ be a (finite or infinite) group such that $G/Z(G)$ is not simple. The non-commuting, non-gen...
Given a class of finite groups, we consider the graph Σ(G) whose vertices are the elements of G and ...
summary:In this paper we consider a prime graph of finite groups. In particular, we expect finite gr...
Let G be a finite group. An element g 08 G is called a vanishing element of G if there exists an ir...
A graph is split if there is a partition of its vertex set into a clique and an independent set. The...
Let G be a finite group, and Irr(G) the set of irreducible complex characters of G. We say that an e...
Let H be a subgroup of a finite non-abelian group G and g∈G. Let Z(H,G)={x∈H:xy=yx,∀y∈G}. We introdu...
AbstractWe prove that in the class graph of a finite group there is no independent set of three vert...
Let G be a non-trivial group. There are many possible ways for associating a graph with G, for the p...
AbstractAssociated with the character degrees of a finite group is the common-divisor graph, where t...
Let G be a finite group, and let cs(G) denote the set of sizes of the conjugacy classes of G. The pr...
Given a 2-generated finite group G, the non-generating graph of G has as vertices the elements of G ...
Given a non-abelian finite group $G$, let $pi(G)$ denote the set of prime divisors of the order of $...
Let G be a finite group. The prime graph of G is the graph whose vertex set is the prime divisors of...
In this paper we consider a prime graph of finite groups. In particular, we expect finite groups wit...
Let $G$ be a (finite or infinite) group such that $G/Z(G)$ is not simple. The non-commuting, non-gen...
Given a class of finite groups, we consider the graph Σ(G) whose vertices are the elements of G and ...
summary:In this paper we consider a prime graph of finite groups. In particular, we expect finite gr...
Let G be a finite group. An element g 08 G is called a vanishing element of G if there exists an ir...
A graph is split if there is a partition of its vertex set into a clique and an independent set. The...
Let G be a finite group, and Irr(G) the set of irreducible complex characters of G. We say that an e...
Let H be a subgroup of a finite non-abelian group G and g∈G. Let Z(H,G)={x∈H:xy=yx,∀y∈G}. We introdu...
AbstractWe prove that in the class graph of a finite group there is no independent set of three vert...
Let G be a non-trivial group. There are many possible ways for associating a graph with G, for the p...
AbstractAssociated with the character degrees of a finite group is the common-divisor graph, where t...
Let G be a finite group, and let cs(G) denote the set of sizes of the conjugacy classes of G. The pr...
Given a 2-generated finite group G, the non-generating graph of G has as vertices the elements of G ...
Given a non-abelian finite group $G$, let $pi(G)$ denote the set of prime divisors of the order of $...
Let G be a finite group. The prime graph of G is the graph whose vertex set is the prime divisors of...