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

^{1}Department of Applied Mathematics, Northwestern Polytechnical University

^{2}Center for Combinatorics and LPMC-TJKLC, Nankai University

^{3}Center 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.

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