Let $G=(V(G),E(G))$ be a digraph without loops and multiarcs, where $V(G)=\{v_1,v_2,$ $\ldots,v_n\}$ and $E(G)$ are the vertex set and the arc set of $G$, respectively. Let $d_i^{+}$ be the outdegree of the vertex $v_i$. Let $A(G)$ be the adjacency matrix of $G$ and $D(G)=\textrm{diag}(d_1^{+},d_2^{+},\ldots,d_n^{+})$ be the diagonal matrix with outdegrees of the vertices of $G$. Then we call $Q(G)=D(G)+A(G)$ the signless Laplacian matrix of $G$. The spectral radius of $Q(G)$ is called the signless Laplacian spectral radius of $G$, denoted by $q(G)$. In this paper, some upper bounds for $q(G)$ are obtained. Furthermore, some upper bounds on $q(G)$ involving outdegrees and the average 2-outdegrees of the vertices of $G$ are also derived.
Xi, W., & Wang, L. (2019). Some upper bounds for the signless Laplacian spectral radius of digraphs. Transactions on Combinatorics, 8(4), 49-60. doi: 10.22108/toc.2019.105894.1515
MLA
Weige Xi; Ligong Wang. "Some upper bounds for the signless Laplacian spectral radius of digraphs". Transactions on Combinatorics, 8, 4, 2019, 49-60. doi: 10.22108/toc.2019.105894.1515
HARVARD
Xi, W., Wang, L. (2019). 'Some upper bounds for the signless Laplacian spectral radius of digraphs', Transactions on Combinatorics, 8(4), pp. 49-60. doi: 10.22108/toc.2019.105894.1515
VANCOUVER
Xi, W., Wang, L. Some upper bounds for the signless Laplacian spectral radius of digraphs. Transactions on Combinatorics, 2019; 8(4): 49-60. doi: 10.22108/toc.2019.105894.1515
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