| A Lower Bound for the Distance Signless Laplacian Spectral Radius of Graphs in Terms of Chromatic Number |
| Received:January 09, 2013 |
| Key Words:
distance matrix distance signless Laplacian spectral radius chromatic number.
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| Fund Project:Supported by National Natural Science Foundation of China (Grant Nos.11071002; 11371028), Program for New Century Excellent Talents in University (Grant No.NCET-10-0001), Key Project of Chinese Ministry of Education (Grant No.210091), Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20103401110002), Natural Science Research Foundation of Department of Education of Anhui Province (Grant No.KJ2013A196) and Scientific Research Fund for Fostering Distinguished Young Scholars of Anhui University (Grant No.KJJQ1001). |
| Author Name | Affiliation | | Xiaoxin LI | Department of Mathematics and Computer Sciences, Chizhou University, Anhui 247000, P. R. China
School of Mathematical Sciences, Anhui University, Anhui 230601, P. R. China | | Yizheng FAN | School of Mathematical Sciences, Anhui University, Anhui 230601, P. R. China | | Shuping ZHA | School of Mathematics and Computation Sciences, Anqing Normal University, Anhui 246011, P. R. China |
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| Abstract: |
| Let $G$ be a connected graph on $n$ vertices with chromatic number $k$, and let $\rho(G)$ be the distance signless Laplacian spectral radius of $G$. We show that $\rho(G) \geq 2n+2\lfloor \frac{n}{k} \rfloor -4$, with equality if and only if $G$ is a regular Tur\'an graph. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.03.004 |
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