论文信息 - The solubility graph associated with a finite group

The solubility graph associated with a finite group

Let $G$ be a finite group. The solubility graph associated with the finite group $G$, denoted by $\Gamma_{\cal S}(G)$, is a simple graph whose vertices are the non-trivial elements of $G$, and there is an edge between two distinct elements $x$ and $y$ if and only if $\langle x, y\rangle$ is a soluble subgroup of $G$. In this paper, we examine some properties of solubility graphs.

[1] L. Dickson. Linear Groups, with an Exposition of the Galois Field Theory , 1958 .

[2] Parthajit Bhowal,et al. A note on solvable graphs of finite groups , 2019, 1903.01755.

[3] R. Guralnick,et al. Thompson-like characterization of the solvable radical , 2005 .

[4] Michio Suzuki. On a finite group with a partition , 1961 .

[5] John G. Thompson. Nonsolvable finite groups all of whose local subgroups are solvable , 1968 .

[6] Mina Hagie. The diameter of the solvable graph of a finite group , 2000 .

[7] B. Huppert. Endliche Gruppen I , 1967 .

[8] Dan Segal,et al. Finite Group Theory , 2003 .

[9] Doron Hai-Reuven. Non-Solvable Graph of a Finite Group and Solvabilizers , 2013, 1307.2924.

[10] N. Iiyori,et al. A generalization of prime graphs of finite groups , 1999 .

[11] Costantino Delizia,et al. Finite groups in which some property of two-generator subgroups is transitive , 2007, Bulletin of the Australian Mathematical Society.

[12] Bertram Huppert,et al. Finite Groups III , 1982 .

[13] R. Guralnick,et al. Thompson-like characterizations of the solvable radical ✩ , 2006 .

[14] Ernest E. Shult,et al. On a class of doubly transitive groups , 1972 .

[15] J. Conway,et al. ATLAS of Finite Groups , 1985 .

[16] Frank Harary,et al. Graph Theory , 2016 .