Let G be a simple graph of order n. The matrix S(G) = D(G) + A(G) is called the signless Laplacian matrix of G, where D(G) and A(G) denote the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively. Let s₁(G) and λ₁(G) be the largest eigenvalue of S(G) and A(G), respectively. In this paper, we first present sharp upper and lower bounds for s₁(G) and λ₁(G) involving the maximum degree, the minimum degree, order, size and sum-connectivity F-index. Moreover, we investigate the relation between s₁(G) and λ₁(G).

中文翻译：

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关于图的邻接矩阵和无符号拉普拉斯矩阵的谱半径

令G为n阶简单图。矩阵S ( G ) =  D ( G ) +  A ( G ) 称为G的无符号拉普拉斯矩阵，其中D ( G ) 和A ( G ) 分别表示顶点度数的对角矩阵和G的邻接矩阵. 令s ₁ ( G ) 和λ ₁ ( G ) 为S ( G ) 和A的最大特征值( G ), 分别。在本文中，我们首先提出了s ₁ ( G ) 和λ ₁ ( G )的上下界，涉及最大度数、最小度数、阶数、大小和总和连通性 F 指数。此外，我们研究了s ₁ ( G ) 和λ ₁ ( G )之间的关系。