Year: 2025
Type: article
Abstract: A graph $G$ has a $\mathcal{P}_{\geq k}$-factor if $G$ has a spanning subgraph $H$ such that every component of $H$ is a path of order at least $k$. A graph $G$ is $\mathcal{P}_{\geq k}$-factor deleted if $G-e$ has a $\mathcal{P}_{\geq k}$-factor for each edge $e \in E(G)$. In this paper, we study the $\mathcal{P}_{\geq 2}$-factor deleted graphs by their $Q$-index (the largest eigenvalue of the signless Laplacian matrix) and $\mathcal{D}$-index (the largest eigenvalue of the distance matrix). Sufficient conditions (in terms of $Q$-index and $\mathcal{D}$-index) to guarantee that a graph $G$ to be a $\mathcal{P}_{\geq 2}$-factor deleted graph are established.
Source: RAIRO - Operations Research
DOI: 10.1051/ro/2025029
Authors: Xiaoyun Lv, Jianxi Li, Shou-Jun Xu
Institutions: Lanzhou University, Minnan Normal University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408539684