4-regular oriented graphs with optimum skew energies

The skew energy of an oriented graph Gσ, denoted by Es(Gσ), is defined as the sum of the singular values of its skew adjacency matrix S(Gσ). The connected k-regular oriented graph on n vertices having skew energy kn is called the optimum skew energy k-regular oriented graph. In this paper, we determ...

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Bibliographic Details
Published in:European journal of combinatorics 2014-02, Vol.36, p.77-85
Main Authors: Gong, Shi-Cai, Xu, Guang-Hui, Zhong, Wen-Bing
Format: Article
Language:English
Subjects:
Byproducts
Combinatorial analysis
Construction
Graphs
Optimization
Orientation
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Summary:The skew energy of an oriented graph Gσ, denoted by Es(Gσ), is defined as the sum of the singular values of its skew adjacency matrix S(Gσ). The connected k-regular oriented graph on n vertices having skew energy kn is called the optimum skew energy k-regular oriented graph. In this paper, we determine the 4-regular graphs G such that each of them has an orientation σ satisfying Gσ which is an optimum skew energy oriented graph. In addition, as by-product we obtain a method to construct optimum skew energy k-regular oriented graphs with large order.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2013.04.010