JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (4): 97-101.doi: 10.6040/j.issn.1671-9352.0.2019.392

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Balaban indices of three kinds of regular graphs

LA Bai1, DENG Bo1,2,3,4,5*, YE Cheng-fu1,4, FU Feng1, LI Yi-jing1   

  1. 1. College of Mathematics and Statistics, Qinghai Normal University, Xining 810008, Qinghai, China;
    2. Tibetan Intelligent Information Processing and Machine Translation Key Laboratory, Xining 810008, Qinghai, China;
    3. Key Laboratory of Tibetan Information Processing and Machine Translation, Qinghai Province, Xining 810008, Qinghai, China;
    4. Academy of Plateau, Science and Sustainability, Xining 810008, Qinghai, China;
    5. College of Science, Guangdong University of Petrochemical Technology, Maoming 525000, Guangdong, China
  • Published:2020-04-09

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Abstract: As an important topological index of a graph, the Balaban index has been widely used in various QSAR(quantitative structure-activity relationship)and QSPR(quantitative structure-property relationship)studies. A lower bound on the Balaban index of a regular graph is given. Then the Balaban index of the small world network graphs, the Cartesian product K2×Ct and a kind of 4-regular graphs produced by the Cartesian product K2×Ct were shown respectively.

Key words: Balaban index, regular graphs, small world network graph, Cartesian product

CLC Number: 

  • O157
[1] BALABAN A T. Highly discriminating distance-based topological index [J]. Chemical Physics Letters, 1982, 89(5): 399-404.
[2] BALABAN A T. Topological indices based on topological distances in molecular graphs [J]. Pure and Applied Chemistry, 1983, 55(2): 199-206.
[3] THAKUR A. QSAR study on benzenesulphonamide carbonic anhydrase inhibitors: topological approach using Balaban index [J]. Bioorganic & Medicinal Chemistry, 2004, 12(4): 789-793.
[4] GRASSY G, CALAS B, YASRI A, et al. Computer-assisted rational design of immunosuppressive compounds [J]. Nature Biotechnology, 1998, 16(8): 748-752.
[5] BERMUDEZ C I, DAZA E E, ANDRADE E. Characterization and comparison of Escherichia coli transfer RNAs by graph theory based on secondary structure [J]. Journal of Theoretical Biology, 1999, 197(2): 193-205.
[6] SHU W J, BO X C, ZHENG Z Q, et al. A novel representation of RNA secondary structure based on element-contact graphs [J]. BMC Bioinformatics, 2008, 9(1): 188.
[7] KNOR M, KRANJC J, SKREKOVSKI R, et al. A search for the minimum value of Balaban index [J]. Applied Mathematics and Computation, 2016, 286: 301-310.
[8] SUN L. Bounds on the Balaban index of trees [J]. MATCH Communications in Mathematical and in Computer Chemistry, 2010, 63(3):813-818.
[9] KNOR M, SKREKOVSKI R, TEPEH A. Balaban index of cubic graphs [J]. MATCH Communications in Mathematical and in Computer Chemistry, 2015, 73(2):519-528.
[10] DONG H W, GUO X F. Character of graphs with extremal Balaban index [J]. MATCH Communications in Mathematical and in Computer Chemistry, 2010, 63(3):799-812.
[11] DENG B, CHANG A. Maximal Balaban index of graphs [J]. MATCH Communications in Mathematical and in Computer Chemistry, 2013, 70(1):259-286.
[12] 邓波, 常彩冰, 王守中, 等. 正则图的Balaban指标[J]. 西南师范大学学报(自然科学版), 2016, 41(6): 12-17. DENG Bo, CHANG Caibing, WANG Shouzhong, et al. On Balaban index of regular graphs [J]. Journal of Southwest China Normal University(Natural Science Edition), 2016, 41(6): 12-17.
[13] PIET V M. Graph spectra for complex networks [M]. Cambridge:Cambridge University Press, 2011: 115-116.
[14] JAHANBAN I A, RAD N J, HASNI R. Pentacyclic graphs with maximum Estrada index [J]. Ars Combin, 2017, 133:133-145.
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