On the determinant of the $Q$-walk matrix of rooted product with a path

Zhidan Yan, Lihuan Mao, Wei Wang

Let $G$ be an $n$-vertex graph and $Q(G)$ be its signless Laplacian matrix. The $Q$-walk matrix of $G$, denoted by $W_Q(G)$, is $[e,Q(G)e,\dots ,Q^{n-1}(G)e]$, where $e$ is the all…