Bounds on the largest eigenvalues of trees with a given size of matching
By Yaoping Hou, Jiongsheng Li. 2002
85 citations recorded by the source corpus.
Very little is known about upper bound for the largest eigenvalue of a tree with a given size of matching. In this paper, we find some upper bounds for the largest eigenvalue of a tree in terms of the number of vertices and the size of matchings, which improve some known results.
Subfields: Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/bc5b82d63c9b845bc3cbc0d719f040dac3283cc7
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In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- Minimum sum-connectivity indices of trees and unicyclic graphs of a given matching number (2010, background): “Lemma 3.2 [16, 17 ] Let G ∈ T(n, m), where n > 2m. Then there is a maximum matching M and a pendant vertex u of G such that u is not M-saturated.”
- A note on the $A_{\alpha}$-spectral radius of graphs (2018, background): “Hou and Li [5] and Guo [4] proved that A(n, k), n ≥ 2k, attains the maximal spectral radius, signless Laplacian spectral radius among all graphs with order n and matching number k, respectively.”