Moreover, the spectral radius of an outerplanar graph on n vertices is less than 1 + √2 + √2 + √n 5.doi:10.1016/0024-3795(93)90139-FDasong CaoAndrew VinceLinear Algebra and its ApplicationsD. Cao, A. Vince: The spectral radius of a planar graph. Linear Algebra Appl., 187 (...
摘要: A decomposition result for planar graphs is used to prove that the spectral radius of a planar graph on n vertices is less than 4 + √ 3 (n 3). Moreover, the spectral radius of an outerplanar graph on n vertices is less than 1 + √2 + √2 + √n 5....
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Upper bounds of the spectral radius of graphs in terms of genus
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Shu, J.L., Hong, Y.: The upper bound for the spectral radius of outerplanar graphs and Halin graphs. Chin. Ann. Math. Ser. A 21, 677–682 (2000) (in Chinese) Stanić, Z.: Inequalities for Graph Eigenvalues, London Mathematical Society Lecture Note Series, vol. 423. Cambridge Unive...
Let H be a connected m-uniform hypergraph, and let A(H) be the adjacency tensor of H whose spectrum is simply called the spectrum of H. Let s(H) denote the number of eigenvectors of A(H) associated with the spectral radius, and c(H) denote the number of eigenvalues of A(H) with...
More precisely, our first main theorem explicitly relates models on the level of partition functions, and probability measures, in the case of finite and infinite graphs. Then, in the planar case, we also rely on the dimer model: we introduce a killed and a drifted dimer model, extending ...
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