On the Dα−spectral radius of two types of graphs

Rui Qin, Dan Li and Jixiang Meng

Applied Mathematics and Computation, 2021, vol. 396, issue C

Abstract: Let D(G) and Tr(G) be the distance matrix and diagonal matrix with vertex transmissions of a connected graph G, separately. Define matrix Dα(G) as Dα(G)=αTr(G)+(1−α)D(G),0≤α≤1. Let Un={G|G is a simple connected graph with |V(G)|=|E(G)|=n},Tn={T|T is a tree of order n} and their complement sets be Unc and Tnc, separately. In this paper, we generalize the conclusions in Qin et al. (2020) to Dα-matrix: we depict the extremal graph with maximum Dα-spectral radius among Unc (n≥8) for any α∈[0,12], and also characterize the graphs among Tnc that reach the maximum and minimum of Dα-spectral radius for any α∈[0,1], respectively.

Keywords: Dα-spectral radius; Complements of graph; Unicyclic graph; Tree; Graft transformation (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:396:y:2021:i:c:s0096300320308511

DOI: 10.1016/j.amc.2020.125898

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