Some upper bounds for the signless Laplacian spectral radius of digraphs
Autor: | Weige Xi, Ligong Wang |
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Jazyk: | angličtina |
Rok vydání: | 2019 |
Předmět: | |
Zdroj: | Transactions on Combinatorics, Vol 8, Iss 4, Pp 49-60 (2019) |
Druh dokumentu: | article |
ISSN: | 2251-8657 2251-8665 |
DOI: | 10.22108/toc.2019.105894.1515 |
Popis: | 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. |
Databáze: | Directory of Open Access Journals |
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