Name
Abstract | ||
|---|---|---|
Motivated by recent progresses on spectral extremal graph theory, in this paper, we aim to investigate the existence of cycles with given length in a graph in terms of its distance spectral radius. First of all, we show that if G is a connected bipartite graph with lambda(1) (D(G)) <= lambda(1)(D(K-1,(n-1))), then G contains a C-4 unless G congruent to K-1,(n-1). When n is sufficiently large with respect to k, as a corollary, we show that S-k(D(G)) >= 2n - 2k if G is a C-4-free bipartite graph. Besides, we prove that S-k(D(G)) >= 2n - 2k if G is a bipartite distance regular graph. These two results partially solve a problem proposed by Lin (2019). Secondly, we give sufficient conditions for the existence of a Hamilton cycle or Hamilton path in a balanced bipartite graph in terms of the distance spectral radius. (C) 2020 Elsevier B.V. All rights reserved. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.dam.2020.09.023 | DISCRETE APPLIED MATHEMATICS |
Keywords | DocType | Volume |
Distance spectral radius, The sum of eigenvalues, Hamilton cycle, Hamilton path | Journal | 289 |
ISSN | Citations | PageRank |
0166-218X | 0 | 0.34 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Huiqiu Lin | 1 | 34 | 11.56 |
| Yuke Zhang | 2 | 0 | 0.68 |