# Sharp Upper Bounds on the Signless Laplacian Spectral Radius of Strongly Connected Digraphs

Discussiones Mathematicae Graph Theory (2016)

- Volume: 36, Issue: 4, page 977-988
- ISSN: 2083-5892

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topWeige Xi, and Ligong Wang. "Sharp Upper Bounds on the Signless Laplacian Spectral Radius of Strongly Connected Digraphs." Discussiones Mathematicae Graph Theory 36.4 (2016): 977-988. <http://eudml.org/doc/287072>.

@article{WeigeXi2016,

abstract = {Let G = (V (G),E(G)) be a simple strongly connected digraph and q(G) be the signless Laplacian spectral radius of G. For any vertex vi ∈ V (G), let d+i denote the outdegree of vi, m+i denote the average 2-outdegree of vi, and N+i denote the set of out-neighbors of vi. In this paper, we prove that: (1) (1) q(G) = d+1 +d+2 , (d+1 ≠ d+2) if and only if G is a star digraph [...] ,where d+1, d+2 are the maximum and the second maximum outdegree, respectively [...] is the digraph on n vertices obtained from a star graph K1,n−1 by replacing each edge with a pair of oppositely directed arcs). (2) [...] with equality if and only if G is a regular digraph. (3) [...] Moreover, the equality holds if and only if G is a regular digraph or a bipartite semiregular digraph. (4) [...] . If the equality holds, then G is a regular digraph or G ∈Ω, where is a class of digraphs defined in this paper.},

author = {Weige Xi, Ligong Wang},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {digraph; signless Laplacian spectral radius},

language = {eng},

number = {4},

pages = {977-988},

title = {Sharp Upper Bounds on the Signless Laplacian Spectral Radius of Strongly Connected Digraphs},

url = {http://eudml.org/doc/287072},

volume = {36},

year = {2016},

}

TY - JOUR

AU - Weige Xi

AU - Ligong Wang

TI - Sharp Upper Bounds on the Signless Laplacian Spectral Radius of Strongly Connected Digraphs

JO - Discussiones Mathematicae Graph Theory

PY - 2016

VL - 36

IS - 4

SP - 977

EP - 988

AB - Let G = (V (G),E(G)) be a simple strongly connected digraph and q(G) be the signless Laplacian spectral radius of G. For any vertex vi ∈ V (G), let d+i denote the outdegree of vi, m+i denote the average 2-outdegree of vi, and N+i denote the set of out-neighbors of vi. In this paper, we prove that: (1) (1) q(G) = d+1 +d+2 , (d+1 ≠ d+2) if and only if G is a star digraph [...] ,where d+1, d+2 are the maximum and the second maximum outdegree, respectively [...] is the digraph on n vertices obtained from a star graph K1,n−1 by replacing each edge with a pair of oppositely directed arcs). (2) [...] with equality if and only if G is a regular digraph. (3) [...] Moreover, the equality holds if and only if G is a regular digraph or a bipartite semiregular digraph. (4) [...] . If the equality holds, then G is a regular digraph or G ∈Ω, where is a class of digraphs defined in this paper.

LA - eng

KW - digraph; signless Laplacian spectral radius

UR - http://eudml.org/doc/287072

ER -

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