On ρ-Tripartite Labeling of Odd Cycles and Some Classes of Complete Tripartite Graphs

Abstract

It is known that a ρ-tripartite labeling of a tripartite graph G with n edges can be used to obtain a cyclic G-decomposition of K2nx+1 for each positive integer x. We show that if G is an odd cycle, then G admits a ρ-tripartite labeling. Furthermore, class of complete tripartite graphs K1,1,n does not admit a ρ-tripartite labeling.