Prime Coloring of Crossing Number Zero Graphs

Abstract

In this paper, prime coloring and its chromatic number of some crossing number zero graphs are depicted and its results are vali-dated with few theorems. Prime Coloring is defined as G be a loop less and Without multiple edges with n distinct Vertices on Color class C={c₁,c₂,c₃,…..c_n} a bijection ψ:V {c₁,c₂,c₃,…..c_n} if for each edge e = c_ic_j ,i≠j , gcd{ ψ (c_i), ψ (c_j)}=1, ψ (c_i) and ψ (c_j) receive distinct Colors. The Chromatic number of Prime coloring is minimum cardinality taken by all the Prime colors. It is denoted by η (G).