Let (G) denote the domination number of a graph G and let G H denote the Cartesian product of graphs G and H. We prove that (G)(H) 2(G H) for all simple graphs G and H. 2000 Math...
We determine the values of the acyclic chromatic index of a class of graphs referred to as d-dimensional partial tori. These are graphs which can be expressed as the cartesian prod...
We consider a class of routing problems on connected graphs G. Initially, each vertex v of G is occupied by a “pebble” which has a unique destination π(v) in G (so that π is...
The first-fit chromatic number of a graph is the number of colors needed in the worst case of a greedy coloring. It is also called the Grundy number, which is defined to be the max...
To each coherent configuration (scheme) C and positive integer m we associate a natural scheme C(m) on the m-fold Cartesian product of the point set of C having the same automorph...