Journal
GRAPHS AND COMBINATORICS
Volume 33, Issue 5, Pages 1283-1295Publisher
SPRINGER JAPAN KK
DOI: 10.1007/s00373-017-1844-x
Keywords
Graph; Laplacian eigenvalue; Domination number
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Funding
- CNPq, Science without Borders, Brazil [400122/2014-6]
- Portuguese Foundation for Science and Technology (FCT-Fundacao para a Ciencia e a Tecnologia), through the CIDMA-Center for Research and Development in Mathematics and Applications [UID/MAT/04106/2013]
- CNPq [409746/2016-9, 303334/2016-9]
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Let denote the number of Laplacian eigenvalues of a graph G in an interval I, and let denote its domination number. We extend the recent result , and show that isolate-free graphs also satisfy . In pursuit of better understanding Laplacian eigenvalue distribution, we find applications for these inequalities. We relate these spectral parameters with the approximability of , showing that . However, gamma(G) <= m(G)[2, n] <= (c + )gamma(G) for c-cyclic graphs, c >= 1. For trees T, gamma(T) <= m(T)[2, n] < 2 gamma(G).
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