Inverse Sum Indeg Energy of Graphs

Abstract

Suppose $G$ is an $n$ -vertex simple graph with vertex set $\{v_{1}, {\dots },v_{n}\}$ and $d_{i}$ , $i=1, {\dots },n$ , is the degree of vertex $v_{i}$ in $G$ . The ISI matrix $S(G)= [s_{ij}]_{n\times n}$ of $G$ is defined by $s_{ij}= \frac {d_{i} d_{j}}{d_{i}+d_{j}}$ if the vertices $v_{i}$ and $v_{j}$ are adjacent and $s_{ij}=0$ otherwise. The $S$ -eigenvalues of $G$ are the eigenvalues of its ISI matrix $S(G)$ . Recently, the notion of inverse sum indeg (henceforth, ISI) energy of graphs is introduced and is defined by $\sum \limits _{i=1}^{n}|\tau _{i}|$ , where $\tau _{i}$ are the $S$ -eigenvalues. We give ISI energy formula of some graph classes. We also obtain some bounds for ISI energy of graphs. In the end, we give some noncospectral equienergetic graphs with respect to inverse sum indeg energy.

Keywords

• Energy of graphs
• inverse sum indeg energy
• extremal bounds
• equienergetic graphs