论文标题
通过其ABC光谱半径订购树木
Ordering Trees by Their ABC Spectral Radii
论文作者
论文摘要
令$ g =（v，e）$为连接的图，其中$ v = \ {v_1，v_2，\ cdots，v_n \} $。令$ d_i $表示顶点$ v_i $的程度。 $ g $的ABC矩阵定义为$ m（g）=（m_ {ij}）_ {n \ times n} $，其中$ m_ {ij} = \ sqrt {（d_i + d_i + d_j -2）/（d_i + d_i d_i d_i d_j）} $ if $ v_i v_i v_j v_j \ $否则， $ g $的ABC光谱半径是$ m（g）$的最大特征值。在本文中，我们就ABC光谱半径建立了两个图扰动。通过施加这些扰动，确定了具有第三，第四和第五大光谱半径的树木。
Let $G=(V,E)$ be a connected graph, where $V=\{v_1, v_2, \cdots, v_n\}$. Let $d_i$ denote the degree of vertex $v_i$. The ABC matrix of $G$ is defined as $M(G)=(m_{ij})_{n \times n}$, where $m_{ij}=\sqrt{(d_i + d_j -2)/(d_i d_j)}$ if $v_i v_j \in E$, and 0 otherwise. The ABC spectral radius of $G$ is the largest eigenvalue of $M(G)$. In the present paper, we establish two graph perturbations with respect to ABC spectral radius. By applying these perturbations, the trees with the third, fourth, and fifth largest ABC spectral radii are determined.
