The extended adjacency matrix of graph $G,$ ${\mathcal{A}}_{ex}$ is a symmetric real matrix that if $i\ne j$ and $u_i{u}_j\in E\left(G\right),$ then the $ij$th entry is $d_{u_i}^2+d_{u_j}^2/2d_{u_i}{d}_{u_j},$ and zero otherwise, where $d_u$ indicates the degree of vertex u. In the present paper, several investigations of the extended adjacency matrix are undertaken and then some spectral properties of ${\mathcal{A}}_{ex}$ are given. Moreover, we present some lower and upper bounds on extended adjacency spectral radii of graphs. Besides, we also study the behavior of the extended adjacency energy of a graph $G$.

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关于扩展邻接矩阵的特征值和能量

图的扩展邻接矩阵 $G，$ ${\mathcal{一种}}_{ËX}$ 是一个对称实矩阵，如果 $\mathrm{一世}\ne Ĵ$ 和 ${ü}_{\mathrm{一世}}{ü}_{Ĵ}\in Ë（G），$ 然后 $\mathrm{一世}Ĵ$条目是 $d_{{ü}_{\mathrm{一世}}}^2+d_{{ü}_{Ĵ}}^2/2d_{{ü}_{\mathrm{一世}}}{d}_{{ü}_{Ĵ}}，$ 否则为零 $d_{ü}$表示顶点度u。在本文中，对扩展邻接矩阵进行了一些研究，然后研究了它们的一些光谱特性。${\mathcal{一种}}_{ËX}$给出。此外，我们给出了图的扩展邻接谱半径的一些上下限。此外，我们还研究了图的扩展邻接能量的行为$G$。