Ordering Trees by Their ABC Spectral Radii

Abstract

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.

References in corpus (1)

• On the Maximum ABC Spectral Radius of Connected Graphs and Trees