TY - JOUR
T1 - A Note on the Determinant of a Special Class of $Q$-Walk Matrices
AU - Tian , Guixian
AU - Wu , Junxing
AU - Cui , Shuyu
AU - Sun , Huilu
JO - Journal of Mathematical Study
VL - 3
SP - 275
EP - 285
PY - 2025
DA - 2025/09
SN - 58
DO - http://doi.org/10.4208/jms.v58n3.25.02
UR - https://global-sci.org/intro/article_detail/jms/24408.html
KW - Signless Laplacian matrix, $Q$-walk matrix, rooted product graph, determinant.
AB - <p style="text-align: justify;">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 $k=2,3.$</p>