An always nontrivial upper bound for Laplacian graph eigenvalues

By Oscar Rojo, Ricardo L. Soto, H. Rojo. 2000

56 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Organic Chemistry

View Paper: https://www.semanticscholar.org/paper/8a3099fa5ffc744c054c1fa039f07c12b2414765

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In Computational Theory and Mathematics

In Geometry and Topology

In Organic Chemistry

Citations in the corpus

Upper bounds on algebraic connectivity via convex optimization (2006, background): “The problem of obtaining lower bounds for the algebraic connectivity and upper bounds for the spectral radius of the Laplacian in terms of various properties of the graph has also been studied; see, for example, [12,17,18,25,20,13].”
An improved upper bound for Laplacian graph eigenvalues (2003, background): “Upper bounds for the largest eigenvalue Rojo [5] has pointed out that sometimes some of these bounds ((1)–(5)) can give trivial results, that is, results which are greater than n, but (6) gives always a nontriv-”
Two sharp upper bounds for the Laplacian eigenvalues (2004, background): “[10] obtained an always nontrivial bound as follows: λ(G) max{d(u)+ d(v)− |N(u) ∩N(v)| |u / = v}, (4) where N(u) is the set of neighbor of u.”
The Laplacian eigenvalues of graphs: a survey (2011, background): “in [83] obtained an always nontrivial upper bound.”
On the Laplacian spectral radius of a tree (2003, background): “[9] have done a lot of work on the Laplacian spectral radius of graphs.”
On the Laplacian spectral radius of a graph (2004, background): “The largest eigenvalue of a matrix M is denoted by λ1(M), while for a graph G ,w e will use λ1(G) to denote λ1(L(G)) and call it the Laplacian spectral radius of G. Recently, some upper bounds for λ1(G) were given by Anderson and Morley [1], Li and Zhang [4,5], Merris [7] and Rojo et al. [ 10 ].”
On the spectral radius of graphs (2004, background): “Up to now, many bounds for ρ(G) and μ(G) were given (see, for instance, [1–12]), but most of them are upper bounds.”
On the Laplacian Eigenvalues of Signed Graphs (2003, background): “5 are not very good because they are the common bounds for the largest eigenvalue of LðG, Þ, perhaps it is better to obtain the bounds which depend on the sign function , such as in [15].”