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- W1984754547 abstract "Let G be a simple graph with n vertices. The matrix L(G)=D(G)−A(G) is called the Laplacian of G, while the matrix Q(G)=D(G)+A(G) is called the signless Laplacian of G, where D(G)=diag(d(v1),d(v2),…,d(vn)) and A(G) denote the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively. Let μ1(G) (resp. λ1(G), q1(G)) be the largest eigenvalue of L(G) (resp. A(G), Q(G)). In this paper, we first present a new upper bound for λ1(G) when each edge of G belongs to at least t(t≥1) triangles. Some new upper and lower bounds on q1(G), q1(G)+q1(Gc) are determined, respectively. We also compare our results in this paper with some known results." @default.
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- W1984754547 date "2012-03-01" @default.
- W1984754547 modified "2023-10-18" @default.
- W1984754547 title "Some bounds on the largest eigenvalues of graphs" @default.
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- W1984754547 doi "https://doi.org/10.1016/j.aml.2011.09.009" @default.
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