Decomposition of complete graphs into tri-cyclic graphs with eight edges

Abstract

In this paper, we use standard graph labeling techniques to prove that each tri-cyclic graph with eight edges decomposes the complete graph \(K_n\) if and only if \(n \equiv 0, 1 \pmod{16}\). We apply \(\rho\)-tripartite labelings and 1-rotational \(\rho\)-tripartite labelings.