On the distance α-spectral radius of a connected graph

Author:

Guo Haiyan,Zhou BoORCID

Abstract

AbstractFor a connected graph G and $\alpha \in [0,1)$α[0,1), the distance α-spectral radius of G is the spectral radius of the matrix $D_{\alpha }(G)$Dα(G) defined as $D_{\alpha }(G)=\alpha T(G)+(1-\alpha )D(G)$Dα(G)=αT(G)+(1α)D(G), where $T(G)$T(G) is a diagonal matrix of vertex transmissions of G and $D(G)$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.

Funder

National Natural Science Foundation of China

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

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