The Divisibility Graph of finite groups of Lie type

The enhanced power graph of a group [Formula: see text] is a simple undirected graph with vertex set [Formula: see text] and two vertices are adjacent if they belong to the same cyclic subgroup. In this paper, we obtain the Laplacian spectrum of the enhanced power graph of certain non-abelian groups, viz. semidihedral, dihedral and generalized quaternion. Also, we obtained the metric dimension and the resolving polynomial of the enhanced power graphs of these groups. At the final part of this paper, we study the distant properties and the detour distant properties, namely: closure, interior, distance degree sequence, eccentric subgraph of the enhanced power graph of semidihedral group, dihedral group and generalized quaternion group, respectively.

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The Divisibility Graph of finite groups of Lie type

Cited by 2 publications

References 32 publications

The Divisibility Graph for F-Groups

The Divisibility Graph for F-Groups

Enhanced power graphs of certain non-abelian groups

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