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On structural properties of ABC-minimal chemical trees

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  • Wu, Xiaoxia
  • Zhang, Lianzhu

Abstract

The atom-bond connectivity (ABC) index of a connected graph G is defined as ABC(G)=∑uv∈E(G)d(u)+d(v)−2d(u)d(v), where d(w) is the degree of vertex w in G and E(G) is the set of edges of G. Given greedy trees perturbed by different degree sequences, we investigate the behaviors on their ABC index in this paper. Moreover, we also give the minimum ABC index and its structural properties of the chemical trees with n vertices and p pendant vertices for n≥3p−2.

Suggested Citation

  • Wu, Xiaoxia & Zhang, Lianzhu, 2019. "On structural properties of ABC-minimal chemical trees," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:362:y:2019:i:c:19
    DOI: 10.1016/j.amc.2019.124570
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    References listed on IDEAS

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    1. Sidje, Roger B. & Stewart, William J., 1999. "A numerical study of large sparse matrix exponentials arising in Markov chains," Computational Statistics & Data Analysis, Elsevier, vol. 29(3), pages 345-368, January.
    2. Dimov, I. & Alexandrov, V. & Karaivanova, A., 2001. "Parallel resolvent Monte Carlo algorithms for linear algebra problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(1), pages 25-35.
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    Cited by:

    1. Das, Kinkar Chandra & Rodríguez, José M. & Sigarreta, José M., 2020. "On the maximal general ABC index of graphs with given maximum degree," Applied Mathematics and Computation, Elsevier, vol. 386(C).

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