• Overview of Chinese core journals
  • Chinese Science Citation Database(CSCD)
  • Chinese Scientific and Technological Paper and Citation Database (CSTPCD)
  • China National Knowledge Infrastructure(CNKI)
  • Chinese Science Abstracts Database(CSAD)
  • JST China
  • SCOPUS
LIU Hechao, WU Rangwei, YOU Lihua. Three Types of Kirchhoff Indices in the Random Cyclooctane Chains[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(2): 96-103. DOI: 10.6054/j.jscnun.2021031
Citation: LIU Hechao, WU Rangwei, YOU Lihua. Three Types of Kirchhoff Indices in the Random Cyclooctane Chains[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(2): 96-103. DOI: 10.6054/j.jscnun.2021031

Three Types of Kirchhoff Indices in the Random Cyclooctane Chains

More Information
  • Received Date: September 28, 2020
  • Available Online: April 28, 2021
  • Using the recursive method, the formula for the expected values of three types of Kirchhoff indices (Kirchhoff index, multiplicative degree-Kirchhoff index and additive degree-Kirchhoff index) in the random cyclooctane chains is first determined. Then the maximum and minimum values of three types of Kirchhoff indices among cyclooctane chains with n octagons (based on this formula) is obtained. All the corresponding extremal graphs are characterized.
  • [1]
    WIENER H. Structural determination of paraffin boiling points[J]. Journal of the American Chemical Society, 1947, 69(1): 17-20. doi: 10.1021/ja01193a005
    [2]
    HOSOYA H. Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons[J]. Bulletin of the Chemi-cal Society of Japan, 1971, 44(9): 2332-2339. doi: 10.1246/bcsj.44.2332
    [3]
    PLAVŠI Ć D, NIKOLI Ć S, TRINAJSTI Ć N, et al. On the Harary index for the characterization of chemical graphs[J]. Journal of Mathematical Chemistry, 1993, 12: 235-250. doi: 10.1007/BF01164638
    [4]
    BONCHEV D, BALABAN A T, LIU X Y, et al. Molecular cyclicity and centricity of polycyclic graphs. I. Cyclicity based on resistance distances or reciprocal distances[J]. International Journal of Quantum Chemistry, 1994, 50(1): 1-20. doi: 10.1002/qua.560500102
    [5]
    WU T Z, LU H Z. Hyper-Wiener indices of polyphenyl chains and polyphenyl spiders[J]. Open Mathematics, 2019, 17(1): 668-676. doi: 10.1515/math-2019-0053
    [6]
    YANG W L, ZHANG F J. Wiener index in random polyphenyl chains[J]. MATCH Communications in Mathematical and in Computer Chemistry, 2012, 68(1): 371-376. http://d.wanfangdata.com.cn/periodical/02a0b21332dbc125b299bf2df835683c
    [7]
    DENG H Y. Wiener indices of spiro and polyphenyl hexagonal chains[J]. Mathematical and Computer Modelling, 2012, 55(3/4): 634-644. http://d.wanfangdata.com.cn/periodical/02a0b21332dbc125b299bf2df835683c
    [8]
    DENG H Y, TANG Z K. Kirchhoff indices of spiro and polyphenyl hexagonal chains[J]. Utilitas Mathematica, 2014, 95: 113-128. http://smartsearch.nstl.gov.cn/paper_detail.html?id=762c56610dade26481ee269cf4932071
    [9]
    WANG H Y, JIANG Q, GUTMAN I. Wiener numbers of random pentagonal chains[J]. Iranian Journal of Mathematical Chemistry, 2013, 4(1): 59-76. http://www.researchgate.net/publication/298092974_Wiener_numbers_of_random_pentagonal_chains
    [10]
    MA L, BIAN H, LIU B J, et al. The expected values of the Wiener indices in the random phenylene and spiro chains[J]. Ars Combinatoria, 2017, 130: 267-274. http://smartsearch.nstl.gov.cn/paper_detail.html?id=c38e709fd0f9bae694afadab6faa0e81
    [11]
    HUANG G H, KUANG M J, DENG H Y. The expected values of Kirchhoff indices in the random polyphenyl and spiro chains[J]. Ars Mathematics Contematica, 2014, 9(2): 197-207. doi: 10.26493/1855-3974.458.7b0
    [12]
    WEI S L, KE X L, WANG Y. Wiener indices in random cyclooctane chains[J]. Wuhan University Journal of Natu-ral Sciences, 2018, 23(6): 498-502. doi: 10.1007/s11859-018-1355-5
    [13]
    ZHANG L L, LI Q S, LI S C, et al. The expected values for the Schultz index, Gutman index, multiplicative degree-Kirchhoff index and additive degree-Kirchhoff index of a random polyphenylene chain[J]. Discrete Applied Mathematics, 2020, 282: 243-256. doi: 10.1016/j.dam.2019.11.007
    [14]
    YANG Y J, JIANG X Y. Unicyclic graphs with extremal Kirchhoff index[J]. MATCH Communications in Mathematical and in Computer Chemistry, 2008, 60(1): 107-120. http://www.researchgate.net/publication/254258266_Unicyclic_graphs_with_extremal_Kirchhoff_index
    [15]
    GUO Q Z, DENG H Y, CHEN D D. The extremal Kirchhoff index of a class of unicyclic graphs[J]. MATCH Communications in Mathematical and in Computer Che-mistry, 2009, 61(3): 713-722. http://www.researchgate.net/publication/266704508_The_extremal_Kirchhoff_index_of_a_class_of_unicyclic_graphs
    [16]
    FENG L H, LIU W J, YU G H, et al. The degree Kirchhoff index of fully loaded unicyclic graphs and cacti[J]. Utili-tas Mathematica, 2014, 95: 149-159. http://smartsearch.nstl.gov.cn/paper_detail.html?id=169152d648bcb79178c4a57157ac0dbb
    [17]
    FEI J Q, TU J H. Complete characterization of bicyclic graphs with the maximum and second-maximum degree Kirchhoff index[J]. Applied Mathematics and Computation, 2018, 330: 118-124. doi: 10.1016/j.amc.2018.02.025
    [18]
    ZHOU B, TRINAJSTI Ć N. On resistance-distance and Kirchhoff index[J]. Journal of Mathematical Chemistry, 2009, 46(1): 283-289. doi: 10.1007/s10910-008-9459-3
    [19]
    YOU Z F, YOU L H, HONG W X. Comment on "Kirchhoff index in line, subdivision and total graphs of a regular graph"[J]. Discrete Applied Mathematics, 2013, 161(18): 3100-3103. doi: 10.1016/j.dam.2013.06.015
    [20]
    WANG H Z, HUA H B, WANG D D. Cacti with minimum, second-minimum, and third-minimum Kirchhoff indices[J]. Mathematical Communications, 2010, 15(2): 347-358. http://www.ams.org/mathscinet-getitem?mr=2814296
    [21]
    TANG Z K, DENG H Y. Degree Kirchhoff index of bicyclic graphs[J]. Canadian Mathematical Bulletin, 2017, 60(1): 197-205. doi: 10.4153/CMB-2016-063-5
    [22]
    KLEIN D J, RANDI Ć M. Resistance distance[J]. Journal of Mathematical Chemistry, 1993, 12(1): 81-95. doi: 10.1007/BF01164627
    [23]
    CHEN H Y, ZHANG F J. Resistance distance and the normalized Laplacian spectrum[J]. Discrete Applied Mathematics, 2017, 155: 654-661. http://www.ams.org/mathscinet-getitem?mr=2303977
    [24]
    GUTMAN I, FENG L H, YU G H. Degree resistance distance of unicyclic graphs[J]. Transactions on Combina-torics, 2012, 1: 27-40. http://www.oalib.com/paper/2304841

Catalog

    Article views (1733) PDF downloads (94) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return