Title: On the sum of Laplacian eigenvalues of a signed graph
Abstract: For a signed graph Γ, let e(Γ) denote the number of edges and Sk(Γ) denote the sum of the k largest eigenvalues of the Laplacian matrix of Γ. We conjecture that for any signed graph Γ with n vertices, Sk(Γ)≤e(Γ)+(k+12)+1 holds for k=1,…,n. We prove the conjecture for any signed graph when k=2, and prove that this conjecture is true for unicyclic and bicyclic signed graphs.
Publication Year: 2018
Publication Date: 2018-10-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 2
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