Graph Energies of Generalized and Shadow-Splitting 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.