Even Vertex Coloring Of A Graph.

Abstract

As a generalization of Harary’s notion of consistency in marked graphs, we define define an even vertex coloring of a graph G as an assignment of colors to the vertices of G such that in every cycle of G there is a nonzero even number of vertices of at least one color. The even vertex coloring number "v(G) of even-vertex colorable graph G is defined as the minimum number of colors in an even vertex coloring of G and a minimum even vertex coloring of G is is one which uses exactly n = "v(G) colors. A characterization of minimally edge-colored graphs is obtained and a result linking the notion to bipartite Eulerian multigraphs is established.