A set of vertices S is a determining set for a graph G if every automorphism of G is uniquely determined by its action on S. The determining number of a graph is the size of a sma...
A map is a connected topological graph cellularly embedded in a surface. For a given graph , its genus distribution of rooted maps and embeddings on orientable and non-orientable s...
Abstract. We study the complexity of the isomorphism and automorphism problems for finite rings. We show that both integer factorization and graph isomorphism reduce to the problem...
Let G be a graph. A vertex labeling of G is distinguishing if the only label-preserving automorphism of G is the identity map. The distinguishing number of G, D(G), is the minimum...