Two sharp upper bounds for the Laplacian eigenvalues
By Xiaodong Zhang. 2004
47 citations recorded by the source corpus.
In this paper, we first obtain a sharp upper bound for the eigenvalues of the adjacency matrix of the line graph of a graph. Then this result is used to present a sharp upper bound for the Laplacian eigenvalues. Another sharp upper bound is presented also. Moreover, we determine all extreme graphs which attain these upper bounds. In last, two examples illustrate that our results are, in some sense, best.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/253e28efbebe8379a5f17bf2b754b6326080a72d
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In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- The Laplacian eigenvalues of graphs: a survey (2011, background): “7 ([96]) Let G be a simple connected graph.”
- Spectral properties of complex unit gain graphs (2011, unknown): “λ1(L( )) max eij∈E { 2 + √ di(di + mi − 4) + dj(dj + mj − 4) + 4 } , [19,13]”