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2016 | 36 | 3 | 695-707
Tytuł artykułu

Nordhaus-Gaddum-Type Results for Resistance Distance-Based Graph Invariants

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Two decades ago, resistance distance was introduced to characterize “chemical distance” in (molecular) graphs. In this paper, we consider three resistance distance-based graph invariants, namely, the Kirchhoff index, the additive degree-Kirchhoff index, and the multiplicative degree-Kirchhoff index. Some Nordhaus-Gaddum-type results for these three molecular structure descriptors are obtained. In addition, a relation between these Kirchhoffian indices is established.
Wydawca
Rocznik
Tom
36
Numer
3
Strony
695-707
Opis fizyczny
Daty
wydano
2016-08-01
otrzymano
2015-03-11
poprawiono
2015-10-31
zaakceptowano
2015-10-31
online
2016-07-06
Twórcy
autor
  • School of Mathematics and Information Science Yantai University Yantai, Shandong, 264005, PR China, yangyj@yahoo.com
autor
  • College of Science Nanjing University of Aeronautics & Astronautics Nanjing, Jiangsu, 210016, PR China, kexxu1221@126.com
Bibliografia
  • [1] D. Bonchev, A.T. Balaban, X. Liu and D.J. Klein, Molecular cyclicity and centricity of polycyclic graphs. I. Cyclicity based on resistance distances or reciprocal distances, Int. J. Quantum Chem. 50 (1994) 1-20. doi:10.1002/qua.560500102[Crossref]
  • [2] H. Chen and F. Zhang, Resistance distance and the normalized Laplacian spectrum, Discrete Appl. Math. 155 (2007) 654-661. doi:10.1016/j.dam.2006.09.008[WoS][Crossref]
  • [3] H. Chen and F. Zhang, Resistance distance local rules, J. Math. Chem. 44 (2008) 405-417. doi:10.1007/s10910-007-9317-8[Crossref]
  • [4] P. Dankelmann, H.C. Swart and P. van den Berg, Diameter and inverse degree, Discrete Math. 308 (2008) 670-673. doi:10.1016/j.disc.2007.07.053[WoS][Crossref]
  • [5] K.Ch. Das, I. Gutman and B. Zhou, New upper bounds on Zagreb indices, J. Math. Chem. 46 (2009) 514-521. doi:10.1007/s10910-008-9475-3[WoS][Crossref]
  • [6] R.M. Foster, The average impedance of an electrical network, in: Contributions to Applied Mechanics (Edwards Bros., Michigan, Ann Arbor, 1949) 333-340.
  • [7] I. Gutman, L. Feng and G. Yu, Degree resistance distance of unicyclic graphs, Trans. Comb. 1 (2012) 27-40.
  • [8] I. Gutman and B. Mohar, The Quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36 (1996) 982-985. doi:10.1021/ci960007t[Crossref]
  • [9] D.J. Klein, Graph geometry, graph metrics, & Wiener , MATCH Commun. Math. Comput. Chem. 35 (1997) 7-27.
  • [10] D.J. Klein, Centrality measure in graphs, J. Math. Chem. 47 (2010) 1209-1223. doi:10.1007/s10910-009-9635-0[Crossref]
  • [11] D.J. Klein and O. Ivanciuc, Graph cyclicity, excess conductance, and resistance deficit , J. Math. Chem. 30 (2001) 271-287. doi:10.1023/A:1015119609980[Crossref]
  • [12] D.J. Klein and M. Randić, Resistance distance, J. Math. Chem. 12 (1993) 81-95. doi:10.1007/BF01164627[Crossref]
  • [13] D.J. Klein and H.-Y. Zhu, Distances and volumina for graphs, J. Math. Chem. 23 (1998) 179-195. doi:10.1023/A:1019108905697[Crossref]
  • [14] E.A. Nordhaus and J.W. Gaddum, On complementary graphs, Amer. Math. Monthly 63 (1956) 175-177. doi:10.2307/2306658[Crossref]
  • [15] J.L. Palacios and J.M. Renom, Another look at the degree-Kirchhoff index , Int. J. Quantum Chem. 111 (2011) 3453-3455. doi:10.1002/qua.22725[Crossref][WoS]
  • [16] H. Wiener, Structural determination of paraffin boiling points, J. Amer. Chem. Soc. 69 (1947) 17-20. doi:10.1021/ja01193a005[Crossref]
  • [17] W. Xiao and I. Gutman, Resistance distance and Laplacian spectrum, Theor. Chem. Acc. 110 (2003) 284-289. doi:10.1007/s00214-003-0460-4[Crossref]
  • [18] Y. Yang, Relations between resistance distances of a graph and its complement or its contraction, Croat. Chem. Acta 87 (2014) 61-68. doi:10.5562/cca2318[WoS][Crossref]
  • [19] Y. Yang, H. Zhang and D.J. Klein, New Nardhaus-Gaddum-type results for the Kirchhoff index , J. Math. Chem. 49 (2011) 1587-1598. doi:10.1007/s10910-011-9845-0[Crossref][WoS]
  • [20] B. Zhou and N. Trinajstić, A note on Kirchhoff index , Chem. Phys. Lett. 455 (2008) 120-123. doi:10.1016/j.cplett.2008.02.060[WoS][Crossref]
  • [21] B. Zhou and N. Trinajstić, On resistance-distance and Kirchhoff index , J. Math. Chem. 46 (2009) 283-289. doi:10.1007/s10910-008-9459-3[WoS][Crossref]
  • [22] H.-Y. Zhu, D.J. Klein and I. Lukovits, Extensions of the Wiener number , J. Chem. Inf. Comput. Sci. 36 (1996) 420-428. doi:10.1021/ci950116s[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1890
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