Inverse sum Indeg index and ISI matrix of graphs

Abstract

Given a graph G = (V, E), the Inverse sum Indeg Index of G, ISI(G) is defined as , where E is the set of edges of G and d is the degree of the vertex u∈V. In this paper, we obtain some bounds of ISI index in terms of some known topological indices. A modification of classical adjacency matrix corresponding to ISI index is proposed and various spectral properties are studied. The new concepts of ISI energy and ISI Estrada index are introduced. We also obtain some bounds of these new graph invariants.

Subject Classification: (2010):

• 05C50
• 05C35

Keywords:

• Inverse sum Indeg
• Graph energy
• Spectral theory