Minimal skew energy of oriented unicyclic graphs with fixed diameter

Let S ( G σ ) be the skew adjacency matrix of the oriented graph G σ , which is obtained from a simple undirected graph G by assigning an orientation σ to each of its edges. The skew energy of an oriented graph G σ is defined as the sum of all singular values of S ( G σ ) . For any positive integer...

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Bibliographic Details
Published in:Journal of inequalities and applications 2013-09, Vol.2013 (1), p.418-418, Article 418
Main Authors: Yang, Xiang-Hao, Gong, Shi-Cai, Xu, Guang-Hui
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:Let S ( G σ ) be the skew adjacency matrix of the oriented graph G σ , which is obtained from a simple undirected graph G by assigning an orientation σ to each of its edges. The skew energy of an oriented graph G σ is defined as the sum of all singular values of S ( G σ ) . For any positive integer d with 3 ≤ d ≤ n − 2 , we in this paper, determine the graph with minimal skew energy among all oriented unicyclic graphs on n vertices with fixed diameter d . MSC: 05C50, 15A18.
ISSN:1029-242X
1029-242X
DOI:10.1186/1029-242X-2013-418