The Maximum Independent Vertex Energy of a Graph

Abstract

In a graph $G=(V, E)$, A set $I\subseteq V$ is an independent vertex set if no two vertices in $I$ are adjacent. The number of vertices in a maximum independent set in a graph $G$ is the independence number (or vertex independence number) of $G$ and is denoted by $\beta(G)$. In this paper, we study the maximum independent vertex energy, denoted by $E_I(G)$, of a graph $G$. We are compute the maximum independent energies of complete graph, complete bipartite graph, star graph, cocktail party graph and Friendship graph. Upper and lower bounds for $E_I(G)$ are established.