We study the energy per vertex in regular graphs. For every k⩾2, we give an upper bound for the energy per vertex of a k -regular graph, and show that a graph attains the upper bound if and only if it is the disjoint union of incidence graphs of projective planes of order k−1 or, in case...

Two standard matrix representations of a graph are the adjacency matrix and the Laplace matrix. The eigenvalues of these matrices are interesting parameters of the graph. Graphs with few eigenvalues in general have nice combinatorial properties and a rich structure. A well investigated family of...