Proof of a conjecture on the determinant of walk matrix of rooted product with a path

Wei Wang, Zhidan Yan, Lihuan Mao

The walk matrix of an $n$-vertex graph $G$ with adjacency matrix $A$, denoted by $W(G)$, is $[e,Ae,\dots ,A^{n-1}e]$, where $e$ is the all-ones vector. Let $G\circ P_m$ be the root…