Degree exponent sum energy of commuting graph for dihedral groups
For a finite group G and a nonempty subset X of G, we construct a graph with a set of vertex X such that any pair of distinct vertices of X are adjacent if they are commuting elements in G. This graph is known as the commuting graph of G on X, denoted by ΓG [X]. The degree exponent sum (DES) matrix...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Published: |
University of Malaya
2022
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/100883/ https://mjs.um.edu.my/index.php/MJS/article/view/34832 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Universiti Putra Malaysia |
| Summary: | For a finite group G and a nonempty subset X of G, we construct a graph with a set of vertex X such that any pair of distinct vertices of X are adjacent if they are commuting elements in G. This graph is known as the commuting graph of G on X, denoted by ΓG [X]. The degree exponent sum (DES) matrix of a graph is a square matrix whose (p,q)-th entry is is dvp dvq + dvqdvp whenever p is different from q, otherwise, it is zero, where dvp (or dvq ) is the degree of the vertex vp (or vertex, vq) of a graph. This study presents results for the DES energy of commuting graph for dihedral groups of order 2n, using the absolute eigenvalues of its DES matrix. |
|---|