It is shown that if a d-regular graph contains s vertices so that the distance between any pair is at least 4k, then its adjacency matrix has at least s eigenvalues which are at l...
Abstract. Given a graph with billions of nodes and edges, how can we find patterns and anomalies? Are there nodes that participate in too many or too few triangles? Are there clos...
For undirected graphs it has been known for some time that one can bound the diameter using the eigenvalues. In this note we give a similar result for the diameter of strongly con...
Let G be a simple graph with n( 2) vertices, and i(G) be the ith largest eigenvalue of G. In this paper we obtain the following: If 3(G) < 0, and there exists some index k, 2 ...