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Li, J., Li, X., Lian, H. (2014). Extremal skew energy of digraphs with no even cycles. Transactions on Combinatorics, 3(1), 37-49. doi: 10.22108/toc.2014.4059
Jing Li; Xueliang Li; Huishu Lian. "Extremal skew energy of digraphs with no even cycles". Transactions on Combinatorics, 3, 1, 2014, 37-49. doi: 10.22108/toc.2014.4059
Li, J., Li, X., Lian, H. (2014). 'Extremal skew energy of digraphs with no even cycles', Transactions on Combinatorics, 3(1), pp. 37-49. doi: 10.22108/toc.2014.4059
Li, J., Li, X., Lian, H. Extremal skew energy of digraphs with no even cycles. Transactions on Combinatorics, 2014; 3(1): 37-49. doi: 10.22108/toc.2014.4059

Extremal skew energy of digraphs with no even cycles

Article 5, Volume 3, Issue 1, March 2014, Page 37-49  XML PDF (223 K)
Document Type: Research Paper
DOI: 10.22108/toc.2014.4059
Authors
Jing Li1; Xueliang Li2; Huishu Lian 3
1Department of Applied Mathematics, Northwestern Polytechnical University
2Center for Combinatorics and LPMC-TJKLC, Nankai University
3Center for Combinatorics, Nankai University
Abstract
‎Let $D$ be a digraph with skew-adjacency matrix $S(D)$‎. ‎Then the‎ ‎skew energy of $D$ is defined as the sum of the norms of all‎ ‎eigenvalues of $S(D)$‎. ‎Denote by $\mathcal{O}_n$ the class of‎ ‎digraphs of order $n$ with no even cycles‎, ‎and by‎ ‎$\mathcal{O}_{n,m}$ the class of digraphs in $\mathcal{O}_n$ with‎ ‎$m$ arcs‎. ‎In this paper‎, ‎we first give the minimal skew energy‎ ‎digraphs in $\mathcal{O}_n$ and $\mathcal{O}_{n,m}$ with $n-1\leq‎ ‎m\leq \frac{3}{2}(n-1)$‎. ‎Then we determine the maximal skew energy‎ ‎digraphs in $\mathcal{O}_{n,n}$ and $\mathcal{O}_{n,n+1}$‎, ‎and in‎ ‎the latter case we assume that $n$ is even‎.
Keywords
skew energy; digraph; signless matching polynomial; Characteristic polynomial
Main Subjects
05C20 Directed graphs (digraphs), tournaments; 05C35 Extremal problems; 05C90 Applications; 15A18 Eigenvalues, singular values, and eigenvectors
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