A labeling of a graph G is distinguishing if it is only preserved by the trivial automorphism of G. The distinguishing chromatic number of G is the smallest integer k such that G ...
The distinguishing number D(G) of a graph G is the least integer d such that G has a labeling with d labels that is preserved only by a trivial automorphism. We prove that Cartesi...
The oriented chromatic number of an oriented graph G is the minimum order of an oriented graph H such that G admits a homomorphism to H. The oriented chromatic number of an undire...
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...
Abstract. Squaregraphs were originally defined as finite plane graphs in which all inner faces are quadrilaterals (i.e., 4-cycles) and all inner vertices (i.e., the vertices not in...