论文标题
群体的广义非策略图
Generalized non-coprime graphs of groups
论文作者
论文摘要
令G为具有身份E和H \ neq \ {e \}的有限组为G。G相对于H的G gamma_ {g，h}的广义非局部图形gamma_ {g，h}相对于H是简单的无向图，g - \ \ \ {e \} \）是顶点和两个不同的vertice a和bc | \ neq 1，在h或b \ in h中a \ a \ in | a |是G中的A \的顺序。在本文中，我们研究了有限基团的普遍非主机图的某些图形理论特性，集中在循环基上。更具体地说，我们获得了循环基团的广义非策略图的必要条件，以使其位于恒星，路径，循环，无三角形，完整的两部分，完整，独轮车，分裂，无爪，弦，弦，弦，弦，弦或完美图。然后，我们表明，将组的类别扩大到所有有限的nilpotent群体都没有给我们任何新图形，但是我们给出了对比行为的一个例子，即EPPO组（所有元素都具有主要功率顺序的eppo组）。我们以与Gruenberg-Kegel图的连接结束。
Let G be a finite group with identity e and H \neq \{e\} be a subgroup of G. The generalized non-coprime graph GAmma_{G,H} of G with respect to H is the simple undirected graph with G - \{e \}\) as the vertex set and two distinct vertices a and b are adjacent if and only if \gcd(|a|,|b|) \neq 1 and either a \in H or b \in H, where |a| is the order of a\in G. In this paper, we study certain graph theoretical properties of generalized non-coprime graphs of finite groups, concentrating on cyclic groups. More specifically, we obtain necessary and sufficient conditions for the generalized non-coprime graph of a cyclic group to be in the class of stars, paths, cycles, triangle-free, complete bipartite, complete, unicycle, split, claw-free, chordal or perfect graphs. Then we show that widening the class of groups to all finite nilpotent groups gives us no new graphs, but we give as an example of contrasting behaviour the class of EPPO groups (those in which all elements have prime power order). We conclude with a connection to the Gruenberg--Kegel graph.
