The (normalized) Laplacian Eigenvalue of Signed Graphs
نویسندگان
چکیده
Abstract. A signed graph Γ = (G, σ) consists of an unsigned graph G = (V, E) and a mapping σ : E → {+,−}. Let Γ be a connected signed graph and L(Γ),L(Γ) be its Laplacian matrix and normalized Laplacian matrix, respectively. Suppose μ1 ≥ · · · ≥ μn−1 ≥ μn ≥ 0 and λ1 ≥ · · · ≥ λn−1 ≥ λn ≥ 0 are the Laplacian eigenvalues and the normalized Laplacian eigenvalues of Γ, respectively. In this paper, we give two new lower bounds on λ1 which are both stronger than Li’s bound [8] and obtain a new upper bound on λn which is also stronger than Li’s bound [8]. In addtion, Hou [6] proposed a conjecture for a
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