Spectral radius and the $2$-power of Hamilton cycles

Abstract

Let $G$ be a graph of order $n$ and spectral radius be the largest eigenvalue of its adjacency matrix, denoted by $\mu (G)$. In this paper, we determine the unique graph with maximum spectral radius among all graphs of order $n$ without containing the $2$-power of a Hamilton cycle.

17 pages, 10 figures