Pseudo-Complete Color Critical Graphs
J. Suresh Kumar · International Journal for Research in Applied Science and Engineering Technology · 2018
A pseudo-complete coloring of a graph G is an assignment of colors to the vertices of G such that for any two distinct colors, there exist adjacent vertices having those colors. The maximum number of colors used in a pseudo-complete coloring of G is called the pseudo-achromatic number of G and is denoted by ( ). A graph G is called edge critical if ( -)< ( )for any edge e of G. A graph G is called vertex critical if ( -) <. ( )for every vertex v of G. These graphs are generally called as pseudo-achromatic number critical graphs (called shortly as PAN Critical graphs). In this paper, we investigate the properties of these critical graphs. We also investigate the locally critical elements of graphs.