Issue |
RAIRO-Oper. Res.
Volume 57, Number 3, May-June 2023
|
|
---|---|---|
Page(s) | 1343 - 1351 | |
DOI | https://doi.org/10.1051/ro/2023069 | |
Published online | 14 June 2023 |
Characterizing an odd [1, b]-factor on the distance signless Laplacian spectral radius
1
School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, P.R. China
2
School of Mathematics and Information Science, Yantai University, Yantai, Shandong 212100, 264005
* Corresponding author: zsz_cumt@163.com
Received:
29
March
2023
Accepted:
19
May
2023
Let G be a connected graph of even order n. An odd [1, b]-factor of G is a spanning subgraph F of G such that dF(v) ∈ {1, 3, 5, ⋯, b} for any v ∈ V(G), where b is positive odd integer. The distance matrix Ɗ(G) of G is a symmetric real matrix with (i, j)-entry being the distance between the vertices vi and vj. The distance signless Laplacian matrix Q(G) of G is defined by Q(G), where Tr(G) is the diagonal matrix of the vertex transmissions in G. The largest eigenvalue η1(G) of Q(G) is called the distance signless Laplacian spectral radius of G. In this paper, we verify sharp upper bounds on the distance signless Laplacian spectral radius to guarantee the existence of an odd [1, b]-factor in a graph; we provide some graphs to show that the bounds are optimal.
Mathematics Subject Classification: 05C70 / 05C50 / 05C35
Key words: Graph / distance signless Laplacian spectral radius / odd [1 b]-factor
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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