The block energy of a graph

In this paper, we introduce the concept block matrix (B-matrix) of a graph \( G \), and obtain some coefficients of the characteristic polynomial \( \phi(G, \mu) \) 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. Let me know if you need additional edits or formatting adjustments!