The Signless Laplacian Spectral Radius of Some Strongly Connected Digraphs

Xihe Li; Ligong Wang; Shangyuan Zhang

doi:10.1007/s13226-018-0257-8

The Signless Laplacian Spectral Radius of Some Strongly Connected Digraphs

Xihe Li, Ligong Wang, Shangyuan Zhang

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let G→ be a strongly connected digraph and Q(G→) be the signless Laplacian matrix of G→. The spectral radius of Q(G→) is called the signless Lapliacian spectral radius of G→. Let ∞˜ ₁-digraph and ∞˜ ₂-digraph be two kinds of generalized strongly connected 1-digraphs and let θ˜ ₁-digraph and 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 ∞˜ ₁-digraphs and θ˜ ₁-digraphs. Furthermore, we characterize the extremal digraph which achieves the maximum signless Laplacian spectral radius among ∞˜ ₂-digraphs and θ˜ ₂-digraphs, respectively.

Original language	English
Pages (from-to)	113-127
Number of pages	15
Journal	Indian Journal of Pure and Applied Mathematics
Volume	49
Issue number	1
DOIs	https://doi.org/10.1007/s13226-018-0257-8
State	Published - 1 Mar 2018

Keywords

The signless Laplacian spectral radius
θ˜ -digraph
θ˜ -digraph
∞˜ -digraph
∞˜ -digraph

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10.1007/s13226-018-0257-8

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abstract = "Let G→ be a strongly connected digraph and Q(G→) be the signless Laplacian matrix of G→. The spectral radius of Q(G→) is called the signless Lapliacian spectral radius of G→. Let ∞˜ 1-digraph and ∞˜ 2-digraph be two kinds of generalized strongly connected 1-digraphs and let θ˜ 1-digraph and 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 ∞˜ 1-digraphs and θ˜ 1-digraphs. Furthermore, we characterize the extremal digraph which achieves the maximum signless Laplacian spectral radius among ∞˜ 2-digraphs and θ˜ 2-digraphs, respectively.",

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N2 - Let G→ be a strongly connected digraph and Q(G→) be the signless Laplacian matrix of G→. The spectral radius of Q(G→) is called the signless Lapliacian spectral radius of G→. Let ∞˜ 1-digraph and ∞˜ 2-digraph be two kinds of generalized strongly connected 1-digraphs and let θ˜ 1-digraph and 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 ∞˜ 1-digraphs and θ˜ 1-digraphs. Furthermore, we characterize the extremal digraph which achieves the maximum signless Laplacian spectral radius among ∞˜ 2-digraphs and θ˜ 2-digraphs, respectively.

AB - Let G→ be a strongly connected digraph and Q(G→) be the signless Laplacian matrix of G→. The spectral radius of Q(G→) is called the signless Lapliacian spectral radius of G→. Let ∞˜ 1-digraph and ∞˜ 2-digraph be two kinds of generalized strongly connected 1-digraphs and let θ˜ 1-digraph and 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 ∞˜ 1-digraphs and θ˜ 1-digraphs. Furthermore, we characterize the extremal digraph which achieves the maximum signless Laplacian spectral radius among ∞˜ 2-digraphs and θ˜ 2-digraphs, respectively.

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The Signless Laplacian Spectral Radius of Some Strongly Connected Digraphs

Abstract

Keywords

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