A general formula for walk determinants of rooted products with applications to DGS-graph constructions

Wei Wang, Jie Shen, Lihuan Mao

For an $n$-vertex graph $G$, and a rooted graph $H^{(v)}$ with $v$ as the root, the rooted product graph $G\circ H^{(v)}$ is obtained from $G$ and $n$ copies of $H$ by identifying…