We derive a new lower bound for the bandwidth of a graph that is based on a new lower bound for the min-cut problem. Our new semidefinite programming relaxation of the min-cut problem is obtained by strengthening the known semidefinite programming relaxation for the quadratic assignment problem...

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...