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A novel method for analyzing inverse problem of topological indices of graphs using competitive agglomeration

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  • Lang, Rongling
  • Li, Tao
  • Mo, Desen
  • Shi, Yongtang

Abstract

A novel method for analyzing the inverse problem of topological indices of graph is proposed in this paper, which applies the data mining technique to classification of graphs according to topological indices. Differing from the way of using topological indices to categorize graphs into different isomorphic classes, this method aims at dividing molecular graphs with n vertices into several compact classes according to their topological indices. Then the chemical and physical features of each kind of graph can be researched and new compounds can be found, which has great significance on bio-medical filed. In the experiment, three classes of simple connected graphs with 5, 6 and 7 vertices, respectively, are investigated and analyzed using the proposed method, the experimental results show the validity of it. However, there are still some problems needed to be researched further, such as selecting the vector of topological indices for clustering, selecting the distance between the vectors of topological indices, choosing the aspects to analyze the properties of each kind of graph after clustering, etc.

Suggested Citation

  • Lang, Rongling & Li, Tao & Mo, Desen & Shi, Yongtang, 2016. "A novel method for analyzing inverse problem of topological indices of graphs using competitive agglomeration," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 115-121.
    • Handle: RePEc:eee:apmaco:v:291:y:2016:i:c:p:115-121
    DOI: 10.1016/j.amc.2016.06.048
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    References listed on IDEAS

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    1. Dehmer, Matthias & Shi, Yongtang & Mowshowitz, Abbe, 2015. "Discrimination power of graph measures based on complex zeros of the partial Hosoya polynomial," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 352-355.
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    6. Matthias Dehmer & Frank Emmert-Streib & Yongtang Shi & Monica Stefu & Shailesh Tripathi, 2015. "Discrimination Power of Polynomial-Based Descriptors for Graphs by Using Functional Matrices," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-10, October.
    7. Ding, Shuai & Wang, Juan & Ruan, Sumei & Xia, Chengyi, 2015. "Inferring to individual diversity promotes the cooperation in the spatial prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 71(C), pages 91-99.
    8. Matthias Dehmer & Abbe Mowshowitz & Yongtang Shi, 2014. "Structural Differentiation of Graphs Using Hosoya-Based Indices," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-4, July.
    9. Dehmer, M. & Moosbrugger, M. & Shi, Y., 2015. "Encoding structural information uniquely with polynomial-based descriptors by employing the Randić matrix," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 164-168.
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    Cited by:

    1. Cao, Shujuan & Dehmer, Matthias & Kang, Zhe, 2017. "Network Entropies Based on Independent Sets and Matchings," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 265-270.
    2. Yu, Guihai & Liu, Xin & Qu, Hui, 2017. "Singularity of Hermitian (quasi-)Laplacian matrix of mixed graphs," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 287-292.
    3. Guihai Yu & Hui Qu, 2018. "More on Spectral Analysis of Signed Networks," Complexity, Hindawi, vol. 2018, pages 1-6, October.
    4. Ji, Shengjin & Liu, Mengmeng & Wu, Jianliang, 2018. "A lower bound of revised Szeged index of bicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 480-487.
    5. Goubko, Mikhail, 2018. "Maximizing Wiener index for trees with given vertex weight and degree sequences," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 102-114.
    6. Li, Fengwei & Ye, Qingfang & Sun, Yuefang, 2017. "On edge-rupture degree of graphs," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 282-293.

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