(untitled) (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−1e], 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. In this note, we establish the relationship between determinants of W_Q(G) and W_Q(G ° P_k ) for k=2,3.