设图$G$是一个简单连通图, $e(G)$、$\mu(G)$和$q(G)$分别为图$G$的边数、谱半径和无符号拉普拉斯谱半径。如果一个图含有一条包含所有顶点的路, 则这条路为哈密尔顿路, 称这个图为可迹图。本文主要研究利用$e(G)$、$\mu(G)$和$q(G)$分别给出图$G$是可迹图的一些新充分条件, 所得结果推广了已有的结论。

Let $G$ be a simple connected graph, $e(G)$, $\mu(G)$ and $q(G)$ be the edge number, the spectral radius and the signless Laplacian spectral radius of the graph $G$, respectively. If a graph has a path which contains all vertices of the graph, the path is called a Hamilton path, the graph is called traceable graph. In this paper, we present some new sufficient conditions for the graph to be traceable graph in terms of $e(G)$, $\mu(G)$ and $q(G)$, respectively. The results generalize the existing conclusions.