On the eigenvalue and energy of extended adjacency matrix

Abstract The extended adjacency matrix of graph G , A e x is a symmetric real matrix that if i ≠ j and u i u j ∈ E ( G ) , then the i j th entry is d u i 2 + d u j 2 / 2 d u i d u j , and zero otherwise, where d u indicates the degree of vertex u. In the present paper, several investigations of the extended adjacency matrix are undertaken and then some spectral properties of A e x are given. Moreover, we present some lower and upper bounds on extended adjacency spectral radii of graphs. Besides, we also study the behavior of the extended adjacency energy of a graph G .