The Chromatic Number and the Least Eigenvalue of a Graph

Abstract

In this paper we get a structural property for a graph having the minimal least eigenvalue among all graphs of fixed order and given chromatic number, and characterize such graphs under the condition that the chromatic number is not larger than half the order of the graph.  As a result, we obtain a lower bound on the least eigenvalue in terms of the chromatic number, and an upper bound on the chromatic number in terms of the least eigenvalue of a graph.