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• # Artykuł - szczegóły

## Discussiones Mathematicae Graph Theory

2016 | 36 | 4 | 977-988

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

EN

### Abstrakty

EN
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.

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977-988

wydano
2016-11-01
otrzymano
2015-03-26
poprawiono
2016-01-13
zaakceptowano
2016-01-13
online
2016-10-21

### Twórcy

autor
• Department of Applied Mathematics School of Science, Northwestern Polytechnical University Xi’an, Shaanxi 710072, P.R.,
autor
• Department of Applied Mathematics School of Science, Northwestern Polytechnical University Xi’an, Shaanxi 710072, P.R.,