A Note on the Determinant of a Special Class of $Q$-Walk Matrices (Journal of Mathematical Study, 2025)
For a graph $G$ of order $n,$ its $Q$-walk matrix is defined by $W_Q(G) = [e,Qe,···,Q^{n−1}e],$ where $Q$ is the signless Laplacian matrix of $G$ and $e$ denotes the all-one column vector. Let $G ° P_k$ represent the rooted product graph of $G$ and a path $P_k.$ Inthis note, we establish the relationship between determinants of $W_Q(G)$ and $W_Q(G ° P_k)$ for $k=2,3.$