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Characteristics polynomial of normalized Laplacian for trees

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  • Banerjee, Anirban
  • Mehatari, Ranjit

Abstract

Here, we find the characteristics polynomial of normalized Laplacian of a tree. The coefficients of this polynomial are expressed by the higher order general Randić indices for matching, whose values depend on the structure of the tree. We also find the expression of these indices for starlike tree and a double-starlike tree, Hm(p, q). Moreover, we show that two cospectral Hm(p, q) of the same diameter are isomorphic.

Suggested Citation

  • Banerjee, Anirban & Mehatari, Ranjit, 2015. "Characteristics polynomial of normalized Laplacian for trees," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 838-844.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:838-844
    DOI: 10.1016/j.amc.2015.09.054
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    References listed on IDEAS

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    1. Mehatari, Ranjit & Banerjee, Anirban, 2015. "Effect on normalized graph Laplacian spectrum by motif attachment and duplication," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 382-387.
    2. Shi, Yongtang, 2015. "Note on two generalizations of the Randić index," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1019-1025.
    3. Tsang, Eric W. K., 2014. "Old and New," Management and Organization Review, Cambridge University Press, vol. 10(03), pages 390-390, November.
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    Cited by:

    1. Cruz, Roberto & Rada, Juan & Sigarreta, José M., 2021. "Sombor index of trees with at most three branch vertices," Applied Mathematics and Computation, Elsevier, vol. 409(C).

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