| Issue |
RAIRO-Oper. Res.
Volume 59, Number 2, March-April 2025
|
|
|---|---|---|
| Page(s) | 1121 - 1140 | |
| DOI | https://doi.org/10.1051/ro/2025029 | |
| Published online | 15 April 2025 | |
Characterizing path-factor deleted graphs via Q-index and D-index
1
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, P.R. China
2
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian, P.R. China
* Corresponding author: shjxu@lzu.edu.cn
Received:
8
April
2024
Accepted:
16
March
2025
A graph G has a P≥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 P≥k-factor deleted if G − e has a P≥k-factor for each edge e ∈ E(G). In this paper, we study the P≥2-factor deleted graphs by their Q-index (the largest eigenvalue of the signless Laplacian matrix) and D-index (the largest eigenvalue of the distance matrix). Sufficient conditions (in terms of Q-index and D-index) to guarantee that a graph G is a P≥2-factor deleted graph are established.
Mathematics Subject Classification: 05C50 / 05C70
Key words: P≥2-factor / P≥2-factor deleted graph / Q-index / D-index
© The authors. Published by EDP Sciences, ROADEF, SMAI 2025
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