Author/Authors :
لي ، ايكسوليانگ نويسنده Center for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin 300071, China Li, Xueliang , كاي ، كينگ كيونگ نويسنده Center for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin 300071, China Cai, Qingqiong , سونگ، جيانگ لي نويسنده Center for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin 300071, China Song, Jiangli
Abstract :
For a simple digraph G of order n with vertex set fv1; v2; : : : ; vng, let d+
i and d??i denote
the out-degree and in-degree of a vertex vi in G, respectively. Let D+(G) = diag(d+
1 ; d+
2 ; : : : ; d+
n ) and
D??(G) = diag(d??1 ; d??2 ; : : : ; d??n ). In this paper we introduce fSL(G) = eD(G)??S(G) to be a new kind of
skew Laplacian matrix of G, where eD(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 fSL(G). Some lower and upper bounds of the new skew Laplacian energy are derived
and the digraphs attaining these bounds are also determined.
