3-Regular digraphs with optimum skew energy

The skew energy of a digraph D is defined as the sum of the singular values of its skew adjacency matrix S ( D ) . In this paper, we first interpret the entries of the power of the skew adjacency matrix of a digraph in terms of the number of its walks and then focus on the question posed by Adiga et...

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Bibliographic Details
Published in:Linear algebra and its applications 2012-02, Vol.436 (3), p.465-471
Main Authors: Gong, Shi-Cai, Xu, Guang-Hui
Format: Article
Language:English
Subjects:
05C50
15A18
Adjacency matrix
Algebra
Combinatorics
Combinatorics. Ordered structures
Digraph
Energy
Exact sciences and technology
Graph theory
Linear and multilinear algebra, matrix theory
Mathematics
Sciences and techniques of general use
Skew energy
Skew-adjacency matrix
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Summary:The skew energy of a digraph D is defined as the sum of the singular values of its skew adjacency matrix S ( D ) . In this paper, we first interpret the entries of the power of the skew adjacency matrix of a digraph in terms of the number of its walks and then focus on the question posed by Adiga et al. [C. Adiga, R. Balakrishnan, Wasin So, The skew energy of a graph, Linear Algebra Appl. 432 (2010) 1825–1835] of determining all 3 -regular connected digraphs with optimum skew energy.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2011.03.067