Spectral conditions for the existence of specified paths and cycles in graphs

Abstract

Let $G$ be a graph with $n$ vertices and $\hat{I}{»}_n(G)$ be the least eigenvalue of its adjacency matrix of $G$. In this paper, we give sharp bounds on the least eigenvalue of graphs without given pathes or cycles and determine the extremal graphs. This result gives spectral conditions for the existence of specified paths and cycles in graphs.