A Note on the Determinant of a Special Class of $Q$-Walk Matrices
Year: 2025
Type: article
Abstract: 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 $G \circ P_k$ 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 $W_Q(G \circ P_k )$ for $k=2,3.$
Source: Journal of Mathematical Study
Authors: Guixian Tian, Junxing Wu, Shuyu Cui, Huilu Sun
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414256941