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Extremal skew energy of digraphs with no even cycles | ||
Transactions on Combinatorics | ||
مقاله 5، دوره 3، شماره 1، خرداد 2014، صفحه 37-49 اصل مقاله (223.22 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2014.4059 | ||
نویسندگان | ||
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 | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
skew energy؛ digraph؛ signless matching polynomial؛ Characteristic polynomial | ||
مراجع | ||
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