Energy of Cartesian Product of graphs K_2 and G with self-loops

Main Article Content

Chunya Tisklang
Kanika Chinphan

Abstract

Let  gif.latex?G_\sigma  be the graph obtained from the simple graph G of order n , by attaching  self-loops to  gif.latex?\sigma  vertices. The energy of the graph gif.latex?G_\sigma denoted by gif.latex?E(G_\sigma) is defined by


        gif.latex?E(G_\sigma)=\sum_{i=1}^n|\lambda_i&space;(G_\sigma)-\frac{\sigma}{n}|


where are the eigenvalues of gif.latex?G_\sigma  for gif.latex?i=1,2,...,n.


In this paper, we study the energy of the cartesian product of the complete graph gif.latex?K_2  and the undirected finite simple graph G  with self-loops denoted by  and we have


gif.latex?E(K_2\times&space;G^l&space;)=&space;\sum_{i=1}^n(|\lambda_i&space;(G)+\frac{\sqrt{5}}{2}|+|\lambda_i&space;(G)-\frac{\sqrt{5}}{2}|)


where gif.latex?\lambda_i(G)  are the eigenvalues of G  for gif.latex?i=1,2,...,n.

Article Details

How to Cite
Tisklang, C., & Chinphan, K. (2025). Energy of Cartesian Product of graphs K_2 and G with self-loops. Rattanakosin Journal of Science and Technology, 7(2), 133–141. retrieved from https://ph02.tci-thaijo.org/index.php/RJST/article/view/253762
Section
Research Articles

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