On the distance α -spectral radius of a connected graph

Journal of inequalities and applications

article

Haiyan Guo¹  Bo Zhou¹ 

[1] School of Mathematical Sciences, South China Normal University

关键词: Distance spectral radius;    Distance signless Laplacian spectral radius;    Local graft transformation;    Extremal graph;   

DOI  :  10.1186/s13660-020-02427-4

学科分类：电力

来源: SpringerOpen

【 摘 要 】

For a connected graph G and $\alpha \in [0,1)$, the distance α-spectral radius of G is the spectral radius of the matrix $D_{\alpha }(G)$ defined as $D_{\alpha }(G)=\alpha T(G)+(1-\alpha )D(G)$, where $T(G)$ is a diagonal matrix of vertex transmissions of G and $D(G)$ is the distance matrix of G. We give bounds for the distance α-spectral radius, especially for graphs that are not transmission regular, propose local graft transformations that decrease or increase the distance α-spectral radius, and determine the graphs that minimize and maximize the distance α-spectral radius among several families of graphs.

【 授权许可】

CC BY