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The chromatic number and the least eigenvalue of a graph
FAN Yizheng,Yu Guidong,WANG Yi
School of Mathematical Sciences, Anhui University
*Correspondence author
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Funding: Science and Technological Fund of Anhui Province for Outstanding Youth (No.10040606Y33), Specialized Research Fund for the Doctoral Program of Higher Education (No.20103401110002), Key Project of Chinese Ministry of Education (No.210091), Scientific Research Fund for Fostering Distinguished Young Scholars of Anhui University(No.KJJQ1001), Academic Innovation Team of Anhui University Project (No.KJTD001B), Fund for Youth Scientific Research of Anhui University(No.KJQN1003), Project of Anhui Province for Excellent Young Talents in Universities (No.2009SQRZ017ZD), National Natural Science Foundation of China (No.11071002)
Opened online:10 June 2011
Accepted by: none
Citation: FAN Yizheng,Yu Guidong,WANG Yi.The chromatic number and the least eigenvalue of a graph[OL]. [10 June 2011] http://en.paper.edu.cn/en_releasepaper/content/4430907
 
 
In this paper we get the structural property for a graph havingthe minimal least eigenvalue among all graphs of order n and given chromatic number x, and characterize such graph under the condition x≤n/2.By the result we obtain a lower bound of the least eigenvalue in terms of chromatic number, and an upper boundof the chromatic number in terms of the least eigenvalue of a graph.
Keywords:Graph; chromatic number; adjacency matrix; least eigenvalue
 
 
 

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