@article {
author = {Oboudi, Mohammad Reza},
title = {Chromatic number and signless Laplacian spectral radius of graphs},
journal = {Transactions on Combinatorics},
volume = {11},
number = {4},
pages = {327-334},
year = {2022},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2021.129720.1876},
abstract = {For any simple graph $G$, the signless Laplacian matrix of $G$ is defined as $D(G)+A(G)$, where $D(G)$ and $A(G)$ are the diagonal matrix of vertex degrees and the adjacency matrix of $G$, respectively. %Let $\chi(G)$ be the chromatic number of $G$ Let $q(G)$ be the signless Laplacian spectral radius of $G$ (the largest eigenvalue of the signless Laplacian matrix of $G$). In this paper we find some relations between the chromatic number and the signless Laplacian spectral radius of graphs. In particular, we characterize all graphs $G$ of order $n$ with odd chromatic number $\chi$ such that $q(G)=2n\Big(1-\frac{1}{\chi}\Big)$. Finally we show that if $G$ is a graph of order $n$ and with chromatic number $\chi$, then under certain conditions, $q(G)<2n\Big(1-\frac{1}{\chi}\Big)-\frac{2}{n}$. This result improves some previous similar results.},
keywords = {chromatic number,Majorization,Signless Laplacian matrix,Signless Laplacian spectral radius},
url = {https://toc.ui.ac.ir/article_26159.html},
eprint = {https://toc.ui.ac.ir/article_26159_fec709a44b419ec4680f4424fb080a49.pdf}
}