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Some results on the distance and distance signless Laplacian spectral radius of graphs and digraphs

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  • Li, Dan
  • Wang, Guoping
  • Meng, Jixiang

Abstract

Let ρ(D(G)) denote the distance spectral radius of a graph G and ∂(G→) denote the distance signless Laplacian spectral radius of a digraph G→. Let Gn,kD be the set of all k-connected graphs of order n with diameter D. In this paper, we first determine the unique graph with minimum distance spectral radius in Gn,kD; we then give sharp upper and lower bounds for the distance signless Laplacian spectral radius of strongly connected digraphs; we also characterize the digraphs having the maximal and minimal distance signless Laplacian spectral radii among all strongly connected digraphs; furthermore, we determine the extremal digraph with the minimal distance signless Laplacian spectral radius with given dichromatic number.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:218-225
    DOI: 10.1016/j.amc.2016.08.025
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    Cited by:

    1. Weige Xi & Lixiang Cai & Wutao Shang & Yidan Su, 2023. "On the General Sum Distance Spectra of Digraphs," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    2. Liu, Kang & Li, Dan & Chen, Yuanyuan & Li, Yuanjing, 2023. "Distance spectral radius of the complements of trees with fixed parameters," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    3. 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).

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