$G$-designs for the connected triangular bicyclic graphs with nine edges

Abstract

A $G$-design of order $n$ is a decomposition of the complete graph $K_n$ into isomorphic copies of $G$. We show that if $G$ is a connected bicyclic graph with nine edges containing two triangles, a $G$-design of order $n$ exists whenever $n \equiv 0,1 \pmod{18}$.

Keywords

• graph decomposition
• bicyclic graphs
• rho-labelings