The Signless Laplacian Spectral Radius of Some Strongly Connected Digraphs

Xihe Li (), Ligong Wang () and Shangyuan Zhang ()
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Xihe Li: Northwestern Polytechnical University
Ligong Wang: Northwestern Polytechnical University
Shangyuan Zhang: Northwestern Polytechnical University

Indian Journal of Pure and Applied Mathematics, 2018, vol. 49, issue 1, 113-127

Abstract: Abstract Let $$\vec G$$ G → be a strongly connected digraph and Q( $$\vec G$$ G → ) be the signless Laplacian matrix of $$\vec G$$ G → . The spectral radius of Q( $$\vec G$$ G → ) is called the signless Lapliacian spectral radius of $$\vec G$$ G → . Let $${\tilde \infty _1}$$ ∞ ˜ 1 -digraph and $${\tilde \infty _2}$$ ∞ ˜ 2 -digraph be two kinds of generalized strongly connected 1-digraphs and let $${\tilde \theta _1}$$ θ ˜ 1 -digraph and $${\tilde \theta _2}$$ θ ˜ 2 -digraph be two kinds of generalized strongly connected µ-digraphs. In this paper, we determine the unique digraph which attains the maximum(or minimum) signless Laplacian spectral radius among all $${\tilde \infty _1}$$ ∞ ˜ 1 -digraphs and $${\tilde \theta _1}$$ θ ˜ 1 -digraphs. Furthermore, we characterize the extremal digraph which achieves the maximum signless Laplacian spectral radius among $${\tilde \infty _2}$$ ∞ ˜ 2 -digraphs and $${\tilde \theta _2}$$ θ ˜ 2 -digraphs, respectively.

Keywords: The signless Laplacian spectral radius; $${\tilde \infty _1}$$ ∞ ˜ 1 -digraph; $${\tilde \infty _2}$$ ∞ ˜ 2 -digraph; $${\tilde \theta _1}$$ θ ˜ 1 -digraph; $${\tilde \theta _2}$$ θ ˜ 2 -digraph (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13226-018-0257-8

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