Energy of Certain Classes of Graphs Determined by Their Laplacian Degree Product Adjacency Spectrum

Asim Khurshid,Mohammad Tariq Rahim,Masood Ur Rehman,Muhammad Salman,Feng Feng

doi:10.1155/2022/5946616

Abstract

In this study, we investigate the Laplacian degree product spectrum and corresponding energy of four families of graphs, namely, complete graphs, complete bipartite graphs, friendship graphs, and corona products of 3 and 4 cycles with a null graph.

Highlights

For energy and spectrum of graph Γ, let A(Γ) be the adjacency matrix, the summation of absolute values of its eigenvalues compose energy of graph and these eigenvalues related with their multiplicities forms the spectrum of graph [4], i.e., Sp(Γ) 􏼠 λ1
We study the Laplacian degree product adjacency spectrum and energy of some well-known families of graphs, such as complete graphs, complete bipartite graphs, friendship graphs, and corona products of 3 and 4 cycles with null graph
We evaluate the correct spectrum and the energy of degree product adjacency matrix of the corona product of 4 cycle with null graphs, which was found incorrect in [6]

Summary

Introduction

For energy and spectrum of graph Γ, let A(Γ) be the adjacency matrix, the summation of absolute values of its eigenvalues compose energy of graph and these eigenvalues related with their multiplicities forms the spectrum of graph [4], i.e., Sp(Γ) 􏼠 λ1. In [6], the degree product adjacency matrix, for a simple connected graph Γ having n vertices say v1, v2, . E Laplacian degree product adjacency matrix of Γ is defined as LDP A(Γ) DP A(Γ) − D(Γ), (5) We evaluate the correct spectrum and the energy of degree product adjacency matrix of the corona product of 4 cycle with null graphs (thorny 4-cycle ring), which was found incorrect in [6].

Results

Conclusion