The block energy of a graph

Abstract

In this paper, we introduce the concept block matrix (B-matrix) of a graph $G$, and obtain some coefficients of the characteristic polynomial $\varphi (G,\mu )$ of the B-matrix of $G$. The block energy $E_B(G)$ is established. Further upper and lower bounds for $E_B(G)$ are obtained. In addition, we define a uni-block graph. Some properties and new bounds for the block energy of the uni-block graph are presented.