We prove a number of relations between the number of cliques of a graph G and the largest eigenvalue (G) of its adjacency matrix. In particular, writing ks (G) for the number of s...
Let µ (G) and µmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) Let G be a regular graph of order n and finite di...
Let µ (G) and µmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) If H is a proper subgraph of a connected graph G o...
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...
Lower bounds on the bandwidth, the size of a vertex separator of general undirected graphs, and the largest common subgraph of two undirected (weighted) graphs are obtained. The b...
Christoph Helmberg, Bojan Mohar, Svatopluk Poljak,...