On the determinant of the walk matrix of the rooted product with a path

Zhidan Yan, Wei Wang

For an $n$-vertex graph $G$, the walk matrix of $G$, denoted by $W(G)$, is the matrix $[e,A(G)e,\dots ,(A(G){)}^{n-1}e]$, where $A(G)$ is the adjacency matrix of $G$ and $e$ is the a…