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On Extended Adjacency Index with Respect to Acyclic, Unicyclic and Bicyclic Graphs

Author

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  • Bin Yang

    (Department of Computer Science and Technology, Hefei University, Hefei 230601, China)

  • Vinayak V. Manjalapur

    (Department of Mathematics, KLE Society’s, Basavaprabhu Kore Arts, Science and Commerce College, Chikodi 591201, Karnataka, India)

  • Sharanu P. Sajjan

    (Department of Computer Science, Government First Grade College for Women, Jamkhandi 587301, India)

  • Madhura M. Mathai

    (Department of Mathematics, KLE Society’s, Raja Lakhamagouda Science Institute, Belgaum 590001, Karnataka, India)

  • Jia-Bao Liu

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

Abstract

For a (molecular) graph G , the extended adjacency index E A ( G ) is defined as Equation (1). In this paper we introduce some graph transformations which increase or decrease the extended adjacency ( E A ) index. Also, we obtain the extremal acyclic, unicyclic and bicyclic graphs with minimum and maximum of the E A index by a unified method, respectively.

Suggested Citation

  • Bin Yang & Vinayak V. Manjalapur & Sharanu P. Sajjan & Madhura M. Mathai & Jia-Bao Liu, 2019. "On Extended Adjacency Index with Respect to Acyclic, Unicyclic and Bicyclic Graphs," Mathematics, MDPI, vol. 7(7), pages 1-9, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:652-:d:250251
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    References listed on IDEAS

    as
    1. Jia-Bao Liu & Bahadur Ali & Muhammad Aslam Malik & Hafiz Muhammad Afzal Siddiqui & Muhammad Imran, 2019. "Reformulated Zagreb Indices of Some Derived Graphs," Mathematics, MDPI, vol. 7(4), pages 1-14, April.
    2. Liu, Jia-Bao & Pan, Xiang-Feng, 2015. "A unified approach to the asymptotic topological indices of various lattices," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 62-73.
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    More about this item

    Keywords

    degree of vertex; extended adjacency index;

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