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

Weige 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 -