Solving the dimer problem of the vertex-edge graph of a cubic graph

Shuli Li, Weigen Yan, Danyi Li

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and $L(G)$ be the line graph of $G$, which has vertex set $E(G)$ and two vertices $e$ and $f$ of $L(G)$ is adjacent i…