It is well-known that eigenvalues of graphs can be used to describe structural properties and parameters of graphs. A theorem of Nosal and Nikiforov states that if $G$ is a triangle-free graph with $m$ edges, then $\lambda (G)\le \sqrt{m}$, equality holds if and only if $G$ is a complete bipartite graph. Recently, Lin, Ning and Wu [Combin. Probab. Comput. 30 (2021)] proved a generalization for non-bipartite triangle-free graphs. Moreover, Zhai and Shu [Discrete Math. 345 (2022)] presented a further improvement. In this paper, we present an alternative method for proving the improvement by Zhai and Shu. Furthermore, the method can allow us to give a refinement on the result of Zhai and Shu for non-bipartite graphs without short odd cycles.
Classification :
05C50, 05C38, 05C35
Mots-clés :
Nosal's theorem, largest spectral radius of triangle-free graph
Affiliations des auteurs :
Yongtao Li
;
Yuejian Peng
1
1
Hunan University
Yongtao Li; Yuejian Peng. The maximum spectral radius of non-bipartite graphs forbidding short odd cycles. The electronic journal of combinatorics, Tome 29 (2022) no. 4. doi: 10.37236/11236
@article{10_37236_11236,
author = {Yongtao Li and Yuejian Peng},
title = {The maximum spectral radius of non-bipartite graphs forbidding short odd cycles},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {4},
doi = {10.37236/11236},
zbl = {1503.05078},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11236/}
}
TY - JOUR
AU - Yongtao Li
AU - Yuejian Peng
TI - The maximum spectral radius of non-bipartite graphs forbidding short odd cycles
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/11236/
DO - 10.37236/11236
ID - 10_37236_11236
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