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Inverse degree and properties of graphs

Funds:  Supported by the Natural Science Foundation of China (11871077), the NSF of Anhui Province (1808085MA04), the NSF of Department of Education of Anhui Province (KJ2017A362).
Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.06.019
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  • Author Bio:

    CAI Gaixiang, female, born in 1981, master/associate Prof. Research field: Graph theory. E-mail: caigaixiang@qq.com

  • Corresponding author: YU Guidong
  • Received Date: 31 March 2020
  • Accepted Date: 10 June 2020
  • Rev Recd Date: 10 June 2020
  • Publish Date: 30 June 2020
    Abstract

  • Abstract

    Let G=(V(G), E(G)) be a simple graph

    Abstract

    Let G=(V(G), E(G)) be a simple graph
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    • References(24)
  • [1]
    XU K, LIU M, DAS K C, et al. A survey on graphs extremal with respect to distance based topological indices[J]. MATCH Commun Math Comput Chem, 2014, 71: 461-508.
    [2]
    GUTMAN I. Degree-based topological indices[J]. Croat Chem Acta, 2013, 86: 351-361.
    [3]
    DAS K C, GUTMAN I, NADJAFIARANI M J. Relations between distance based and degree based topological indices[J]. Appl Math Comput, 2015, 270: 142-147.
    [4]
    FAJTLOWICZ S. On conjectures of Graffiti II[J]. Congr Numer, 1987, 60:189-197.
    [5]
    ZHANG Z, ZHANG J, LU X. The relation of matching with inverse degree of a graph[J]. Discrete Math, 2005, 301: 243-246.
    [6]
    HU Y, LI X, XU T. Connected (n; m) graphs with minimum and maximum zeroth-order Randic＇ index[J]. Discrete Appl Math, 2007, 155: 1044-1054.
    [7]
    DANKELMANN P, HELLWIG A, VOLKMANN L. Inverse degree and edge-connectivity[J]. Discrete Math, 2009, 309: 2943-2947.
    [8]
    MUKWEMBI S. On diameter and inverse degree of a graph[J]. Discrete Math, 2010, 310: 940-946.
    [9]
    LI X, SHI Y. On the diameter and inverse degree[J]. Ars Combin, 2011, 101: 481- 487.
    [10]
    CHEN X, FUJITA S. On diameter and inverse degree of chemical graphs[J]. Appl Anal Discrete Math, 2013, 7: 83-93.
    [11]
    XU K, DAS K C. Some extremal graphs with respect to inverse degree[J]. Discrete Appl Math, 2016, 203: 171-183.
    [12]
    DAS K C, XU K, WANG J. On inverse degree and topological indices of graphs[J]. Filomat, 2016, 30: 2111-2120.
    [13]
    DAS K C, BALACHANDRAN S, GUTMAN I. Inverse degree, Randic＇ index and harmonic index of graphs[J]. Appl Anal Discrete Math, 2017, 11(2): 304-313.
    [14]
    ELUMALAI S, HOSAMANI S M, MANSOUR T, et al. More on inverse degree and topological indices of graphs[J]. Filomat, 2018, 32(1): 165-178.
    [15]
    CHVTAL V. On Hamiltons ideals[J]. J Combin Theory Ser B, 1972, 12: 163-168.
    [16]
    KRONK H V. A note on k-path Hamiltonian graphs[J]. J Combin Theory, 1969, 7: 104-106.
    [17]
    BONDY J A , CHVTAL V. A method in graph theory[J]. Discrete Math, 1976, 15: 111-135.
    [18]
    YU G D, YE M L, CAI G X, et al. Signless Laplacian spectral conditions for Hamiltonicity of graphs[J]. Journal of Applied Mathematics, 2014, 2014: Article ID 282053.
    [19]
    BONDY J A. Properties of graphs with constraints on degrees[J]. Studia Sci Math Hungar, 1969, 4: 473-475.
    [20]
    BAUER D, HAKIMI S L, KAHL N, et al. Sufficient degree conditions for k-edge-connectedness of a graph[J]. Networks, 2009, 54: 95-98.
    [21]
    LAS VERGNAS M. Problèmes de couplages et problèmes Hamiltoniens en théorie des graphes[D]. Paris: Université Pierre-et-Marie-Curie, 1972.
    [22]
    BAUER D, BROERSMA H J, VAN DEN HEUVEL J, et al. Best monotone degree conditions for graph properties: A survey[J]. Graphs Combin, 2015, 31: 1-22.
    [23]
    BERGE C. Graphs and Hypergraphs[M]. Amsterdam: North-Holland, 1973.
    [24]
    FENG L, ZHANG P, LIU H, et al. Spectral conditions for some graphical properties[J]. Linear Algebra and Its Applications, 2017, 524: 182-198.)
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    [1]
    XU K, LIU M, DAS K C, et al. A survey on graphs extremal with respect to distance based topological indices[J]. MATCH Commun Math Comput Chem, 2014, 71: 461-508.
    [2]
    GUTMAN I. Degree-based topological indices[J]. Croat Chem Acta, 2013, 86: 351-361.
    [3]
    DAS K C, GUTMAN I, NADJAFIARANI M J. Relations between distance based and degree based topological indices[J]. Appl Math Comput, 2015, 270: 142-147.
    [4]
    FAJTLOWICZ S. On conjectures of Graffiti II[J]. Congr Numer, 1987, 60:189-197.
    [5]
    ZHANG Z, ZHANG J, LU X. The relation of matching with inverse degree of a graph[J]. Discrete Math, 2005, 301: 243-246.
    [6]
    HU Y, LI X, XU T. Connected (n; m) graphs with minimum and maximum zeroth-order Randic＇ index[J]. Discrete Appl Math, 2007, 155: 1044-1054.
    [7]
    DANKELMANN P, HELLWIG A, VOLKMANN L. Inverse degree and edge-connectivity[J]. Discrete Math, 2009, 309: 2943-2947.
    [8]
    MUKWEMBI S. On diameter and inverse degree of a graph[J]. Discrete Math, 2010, 310: 940-946.
    [9]
    LI X, SHI Y. On the diameter and inverse degree[J]. Ars Combin, 2011, 101: 481- 487.
    [10]
    CHEN X, FUJITA S. On diameter and inverse degree of chemical graphs[J]. Appl Anal Discrete Math, 2013, 7: 83-93.
    [11]
    XU K, DAS K C. Some extremal graphs with respect to inverse degree[J]. Discrete Appl Math, 2016, 203: 171-183.
    [12]
    DAS K C, XU K, WANG J. On inverse degree and topological indices of graphs[J]. Filomat, 2016, 30: 2111-2120.
    [13]
    DAS K C, BALACHANDRAN S, GUTMAN I. Inverse degree, Randic＇ index and harmonic index of graphs[J]. Appl Anal Discrete Math, 2017, 11(2): 304-313.
    [14]
    ELUMALAI S, HOSAMANI S M, MANSOUR T, et al. More on inverse degree and topological indices of graphs[J]. Filomat, 2018, 32(1): 165-178.
    [15]
    CHVTAL V. On Hamiltons ideals[J]. J Combin Theory Ser B, 1972, 12: 163-168.
    [16]
    KRONK H V. A note on k-path Hamiltonian graphs[J]. J Combin Theory, 1969, 7: 104-106.
    [17]
    BONDY J A , CHVTAL V. A method in graph theory[J]. Discrete Math, 1976, 15: 111-135.
    [18]
    YU G D, YE M L, CAI G X, et al. Signless Laplacian spectral conditions for Hamiltonicity of graphs[J]. Journal of Applied Mathematics, 2014, 2014: Article ID 282053.
    [19]
    BONDY J A. Properties of graphs with constraints on degrees[J]. Studia Sci Math Hungar, 1969, 4: 473-475.
    [20]
    BAUER D, HAKIMI S L, KAHL N, et al. Sufficient degree conditions for k-edge-connectedness of a graph[J]. Networks, 2009, 54: 95-98.
    [21]
    LAS VERGNAS M. Problèmes de couplages et problèmes Hamiltoniens en théorie des graphes[D]. Paris: Université Pierre-et-Marie-Curie, 1972.
    [22]
    BAUER D, BROERSMA H J, VAN DEN HEUVEL J, et al. Best monotone degree conditions for graph properties: A survey[J]. Graphs Combin, 2015, 31: 1-22.
    [23]
    BERGE C. Graphs and Hypergraphs[M]. Amsterdam: North-Holland, 1973.
    [24]
    FENG L, ZHANG P, LIU H, et al. Spectral conditions for some graphical properties[J]. Linear Algebra and Its Applications, 2017, 524: 182-198.)
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