D. Cvetković, M. Doob and H. Sachs considered the high order eigenvalue problems of graphs. The high order eigenvalues of a graph G are solutions of the high degree homogeneous polynomial equations derived from G. We propose the adjacency tensor $\mathcal{A}(G)$ of a graph G and show that the high order eigenvalues of G can be regarded as eigenvalues of $\mathcal{A}(G)$. Some results of the spectrum of the adjacency matrix are extended to the spectrum of $\mathcal{A}(G)$ by using the spectral theory of nonnegative tensors. An upper bound of chromatic number is given via the spectral radius of $\mathcal{A}(G)$. Our upper bound is a generalization of Wilf's bound $\chi (G)\le \rho (G)+1$ (where $\rho (G)$ is the spectral radius of the adjacency matrix of a graph G) and sharper than the bound of Wilf in some classes of graphs. A formula of the number of cliques of fixed size which involve the spectrum of $\mathcal{A}(G)$ is obtained.

D. Cvetković、M. Doob 和 H. Sachs 考虑了图的高阶特征值问题。图G的高阶特征值是从G导出的高次齐次多项式方程的解。我们提出邻接张量$\mathcal{A}（G）$图G的特征值，并表明G的高阶特征值可以视为$\mathcal{A}（G）$。将邻接矩阵的谱的一些结果推广到$\mathcal{A}（G）$通过使用非负张量的谱理论。色数的上限通过光谱半径给出$\mathcal{A}（G）$。我们的上限是 Wilf 界限的推广$\chi （G）\le \rho （G）+1$（在哪里$\rho （G）$是图G的邻接矩阵的谱半径，并且在某些类别的图中比 Wilf 的界限更尖锐。固定大小的派系数量的公式，涉及的频谱$\mathcal{A}（G）$获得。