Randic Type Hadi Energy of a Graph

Abstract

Randić index is one of the most famous topological graph indices. The energy of a graph was defined more than four decades ago for its molecular applications. The classical energy of a graph modeling a molecule is defined as the sum of absolute values of all the eigenvalues of the adjacency matrix corresponding to the modeling graph. There are several other versions of the energy notion obtained using other types of graph matrices. In this paper, we are introducing and investigating the Randić type Hadi energy RHE(G) of a graph G, determine several properties of it, and calculate RHE(G) for several interesting graphs.