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On the Dα−spectral radius of two types of graphs

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  • Qin, Rui
  • Li, Dan
  • Meng, Jixiang

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.

Suggested Citation

  • Qin, Rui & Li, Dan & Meng, Jixiang, 2021. "On the Dα−spectral radius of two types of graphs," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    • Handle: RePEc:eee:apmaco:v:396:y:2021:i:c:s0096300320308511
    DOI: 10.1016/j.amc.2020.125898
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    References listed on IDEAS

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    1. Li, Dan & Wang, Guoping & Meng, Jixiang, 2017. "Some results on the distance and distance signless Laplacian spectral radius of graphs and digraphs," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 218-225.
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