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- Title
Enhanced power graphs of certain non-abelian groups.
- Authors
Parveen; Dalal, Sandeep; Kumar, Jitender
- Abstract
The enhanced power graph of a group G is a simple undirected graph with vertex set G 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.
- Subjects
NONABELIAN groups; UNDIRECTED graphs; POWER spectra; LAPLACIAN matrices; FINITE groups; QUATERNIONS; POLYNOMIALS
- Publication
Discrete Mathematics, Algorithms & Applications, 2024, Vol 16, Issue 5, p1
- ISSN
1793-8309
- Publication type
Article
- DOI
10.1142/S1793830923500635