On the distance α-spectral radius of a connected graph

01/29/2019

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by   H. Y. Guo, et al.

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For a connected graph G and α∈ [0,1), the distance α-spectral radius of G is the spectral radius of the matrix D_α(G) defined as D_α(G)=α T(G)+(1-α)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 some graft transformations that decrease or increase the distance α-spectral radius, and determine the unique graphs with minimum and maximum distance α-spectral radius among some classes of graphs.