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New skew Laplacian energy of simple digraphs | ||
| Transactions on Combinatorics | ||
| مقاله 1، دوره 2، شماره 1، خرداد 2013، صفحه 27-37 اصل مقاله (495.2 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2013.2833 | ||
| نویسندگان | ||
| Qingqiong Cai1؛ Xueliang Li* 2؛ Jiangli Song3 | ||
| 1Center for Combinatorics, nankai University, Tianjin, China | ||
| 2Center for Combinatorics, Nankai University, Tianjin 300071, China | ||
| 3Center for Combinatorics, Nankai University, Tianjin, China | ||
| چکیده | ||
| For a simple digraph $G$ of order $n$ with vertex set $\{v_1,v_2,\ldots, v_n\}$, let $d_i^+$ and $d_i^-$ denote the out-degree and in-degree of a vertex $v_i$ in $G$, respectively. Let $D^+(G)=diag(d_1^+,d_2^+,\ldots,d_n^+)$ and $D^-(G)=diag(d_1^-,d_2^-,\ldots,d_n^-)$. In this paper we introduce $\widetilde{SL}(G)=\widetilde{D}(G)-S(G)$ to be a new kind of skew Laplacian matrix of $G$, where $\widetilde{D}(G)=D^+(G)-D^-(G)$ and $S(G)$ is the skew-adjacency matrix of $G$, and from which we define the skew Laplacian energy $SLE(G)$ of $G$ as the sum of the norms of all the eigenvalues of $\widetilde{SL}(G)$. Some lower and upper bounds of the new skew Laplacian energy are derived and the digraphs attaining these bounds are also determined. | ||
| کلیدواژه‌ها | ||
| energy؛ Laplacian energy؛ skew energy؛ skew Laplacian energy؛ eigenvalues | ||
| مراجع | ||
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