Graph Energies of Generalized and Shadow-Splitting Graphs

TL;DR

This paper introduces new graph operations called generalized splitting and shadow-splitting graphs, derives their adjacency energy, and identifies new families of equienergetic and borderenergetic graphs.

Contribution

It extends existing graph notions to define new operations and analyzes their energies, leading to the discovery of novel equienergetic graph families.

Findings

Derived the adjacency energy of the new graph constructions.

Identified several infinite families of equienergetic and borderenergetic graphs.

Abstract

We extend the notions of the m-splitting graph Sm(G) and the m-shadow graph Dm(G) to introduce two new graph operations: the (p, q)-generalized splitting graph Sp,q(G) and the (c, k)-shadow-splitting graph Hc,k(G). We derive the adjacency energy of these constructions and as an application, identify several new infinite families of equienergetic and borderenergetic graphs.