Physical Sciences and Mathematics Commons^™

The Set Chromatic Numbers Of The Middle Graph Of Graphs, Gerone Russel J. Eugenio, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino

Mathematics Faculty Publications

For a simple connected graph G; let c : V (G) → N be a vertex coloring of G; where adjacent vertices may be colored the same. The neighborhood color set of a vertex v; denoted by NC(v); is the set of colors of the neighbors of v. The coloring c is called a set coloring provided that NC(u) neq NC(v) for every pair of adjacent vertices u and v of G. The minimum number of colors needed for a set coloring of G is referred to as the set chromatic number of G and is denoted by χ_s(G). In …