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Permanental Bounds of the Laplacian Matrix of Trees with Given Domination Number

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Let \(\fancyscript{T}_{n,\gamma }\) be the collection of all \(n\)-vertex trees with domination number \(\gamma \). In this paper, the first-, second- and third-smallest Laplacian permanents of trees in \(\fancyscript{T}_{n,\gamma }\) are determined, respectively. Moreover, the corresponding extremal graphs are characterized.

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Acknowledgments

Financially supported by the National Natural Science Foundation of China (Grant Nos. 11271149, 11371062), the Program for New Century Excellent Talents in University (Grant No. NCET-13-0817) and the Special Fund for Basic Scientific Research of Central Colleges (Grant No. CCNU13F020).

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Correspondence to Shuchao Li.

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Geng, X., Hu, S. & Li, S. Permanental Bounds of the Laplacian Matrix of Trees with Given Domination Number. Graphs and Combinatorics 31, 1423–1436 (2015). https://doi.org/10.1007/s00373-014-1451-z

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  • DOI: https://doi.org/10.1007/s00373-014-1451-z

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