Distance and Adjacency Energies of Multi-Level Wheel Networks

Jia-Bao Liu,Mobeen Munir,Asim Naseem,Amina Yousaf,Khudaija Ayub

doi:10.3390/math7010043

Abstract

Energies of molecular graphs have various applications in chemistry, polymerization, computer networking and pharmacy. In this paper, we give general closed forms of distance and adjacency energies of generalized wheel networks W n , m . Consequently, we give these results for classical wheel graphs. We also give pictorial dependencies of energies on the involved parameters m ≥ 3 and n .

Highlights

Energy is referred to as the sum of absolute values of any operator
Where α and β are the empirical constants of Huckel molecular orbital theory and A( G ) is the adjacency matrix of the Huckel graph constructed for the π-electron network of conjugated hydro-carbons [1]
The ordinary energy of the graph is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix

Summary

Introduction

Energy is referred to as the sum of absolute values of any operator. In quantum chemistry, the solutions of the Schrodinger equation is approximately reduced to the evaluation of eigenvalues and corresponding eigenvectors of the Hamiltonian operator. The ordinary energy of the graph is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. In [6], authors computed general forms of energies of non-regular graphs. Developed, a model resulting in a fact that the roots of the characteristic polynomial of the line graph of the molecular graph are in a linear manner related to the s-electron energy levels of the corresponding

Results

Conclusion