On spectral radius and energy of extended adjacency matrix of graphs.

Let G be a graph of order n . For i = 1 , 2 , … , n , let d i be the degree of the vertex v i of G . The extended adjacency matrix A ex of G is defined so that its ( i, j )-entry is equal to 1 2 ( d i d j + d j d i ) if the vertices v i and v j are adjacent, and 0 otherwise,Yang et al. (1994). The spectral radius η 1 and the energy E e x of the A ex -matrix are examined. Lower and upper bounds on η 1 and E e x are obtained, and the respective extremal graphs characterized. [ABSTRACT FROM AUTHOR]