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 $n\equiv 0,1(\mathrm{mod}16)$. We apply $\rho$-tripartite labelings and 1-rotational $\rho$-tripartite labelings.