On the distance spectrum and distance-based topological indices of central vertex-edge join of three graphs

TL;DR

This paper introduces a new graph operation called the central vertex-edge join, analyzes its impact on various topological indices and distance spectrum, and constructs new families of D-eneergetic graphs.

Contribution

It presents the central vertex-edge join operation, studies its effects on multiple graph invariants, and explores the distance spectrum and D-eneergetic graph families.

Findings

Derived formulas for topological indices of the join

Analyzed the distance spectrum of the join of three regular graphs

Constructed new non D-cospectral D-eneergetic graphs

Abstract

Topological indices are molecular descriptors that describe the properties of chemical compounds. These topological indices correlate specific physico-chemical properties like boiling point, enthalpy of vaporization, strain energy, and stability of chemical compounds. This article introduces a new graph operation based on central graph called central vertex-edge join and provides its results related to graph invariants like eccentric-connectivity index, connective eccentricity index, total-eccentricity index, average eccentricity index, Zagreb eccentricity indices, eccentric geometric-arithmetic index, eccentric atom-bond connectivity index, and Wiener index. Also, we discuss the distance spectrum of the central vertex-edge join of three regular graphs. Furthermore, we obtain new families of $D$-equienergetic graphs, which are non $D$-cospectral.