Spectral Properties with the Difference between Topological Indices in Graphs

Abstract EN

Let G be a graph of order n with vertices labeled as v1,v2,…,vn.

Let di be the degree of the vertex vi, for i=1,2,…,n.

The difference adjacency matrix of G is the square matrix of order n whose i,j entry is equal to di+dj−2−1/didj if the vertices vi and vj of G are adjacent or vivj∈EG and zero otherwise.

Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix, that is, a modification of the classical adjacency matrix involving the degrees of the vertices.

In this paper, some properties of its characteristic polynomial are studied.

We also investigate the difference energy of a graph.

In addition, we establish some upper and lower bounds for this new energy of graph.