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Volumn 36, Issue 2, 2013, Pages 373-383

Extremal Unicyclic and Bicyclic graphs with respect to Harary index

Author keywords

Bicyclic graph; Diameter; Harary index; Unicyclic graph

Indexed keywords


EID: 84880107765     PISSN: 01266705     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (40)

References (34)
  • 4
    • 70350140206 scopus 로고    scopus 로고
    • Bounds on Harary index
    • K. Ch. Das, B. Zhou and N. Trinajstić, Bounds on Harary index, J. Math. Chem. 46 (2009), no. 4, 1377-1393.
    • (2009) J. Math. Chem , vol.46 , Issue.4 , pp. 1377-1393
    • Das, K.C.1    Zhou, B.2    Trinajstić, N.3
  • 6
    • 34247114228 scopus 로고    scopus 로고
    • The trees on n ≥ 9 vertices with the first to seventeenth greatest Wiener indices are chemical trees
    • H.-Y. Deng, The trees on n ≥ 9 vertices with the first to seventeenth greatest Wiener indices are chemical trees, MATCH Commun. Math. Comput. Chem. 57 (2007), no. 2, 393-402.
    • (2007) MATCH Commun. Math. Comput. Chem , vol.57 , Issue.2 , pp. 393-402
    • Deng, H.-Y.1
  • 7
    • 0035329265 scopus 로고    scopus 로고
    • Wiener index of trees: Theory and applications
    • A. A. Dobrynin, R. Entringer and I. Gutman, Wiener index of trees: Theory and applications, Acta Appl. Math. 66 (2001), no. 3, 211-249.
    • (2001) Acta Appl. Math , vol.66 , Issue.3 , pp. 211-249
    • Dobrynin, A.A.1    Entringer, R.2    Gutman, I.3
  • 9
    • 84867739163 scopus 로고    scopus 로고
    • The relationships between Wiener index, stability number and clique number of composite graphs
    • T. Došlic, M. Ghorbani and M. A. Hosseinzadeh, The relationships between Wiener index, stability number and clique number of composite graphs, Bull. Malays. Math. Sci. Soc. (2) 36 (2013), no. 1, 165-172.
    • (2013) Bull. Malays. Math. Sci. Soc. (2) , vol.36 , Issue.1 , pp. 165-172
    • Došlic, T.1    Ghorbani, M.2    Hosseinzadeh, M.A.3
  • 11
    • 84858014840 scopus 로고    scopus 로고
    • Zagreb, Harary and hyper-Wiener indices of graphs with a given matching number
    • L. Feng and A. Ilić, Zagreb, Harary and hyper-Wiener indices of graphs with a given matching number, Appl. Math. Lett. 23 (2010), no. 8, 943-948.
    • (2010) Appl. Math. Lett , vol.23 , Issue.8 , pp. 943-948
    • Feng, L.1    Ilić, A.2
  • 15
    • 0037020059 scopus 로고    scopus 로고
    • Relation between hyper-Wiener and Wiener index
    • I. Gutman, Relation between hyper-Wiener and Wiener index, Chem. Phys. Lett. 364 (2002), 352-356.
    • (2002) Chem. Phys. Lett , vol.364 , pp. 352-356
    • Gutman, I.1
  • 16
    • 2542583389 scopus 로고    scopus 로고
    • A property of the Wiener number and its modifications
    • I. Gutman, A property of the Wiener number and its modifications, Indian J. Chem. A 36 (1997), 128-132.
    • (1997) Indian J. Chem. A , vol.36 , pp. 128-132
    • Gutman, I.1
  • 17
    • 0038796083 scopus 로고    scopus 로고
    • Hyper-Wiener index vs. Wiener index. Two highly correlated structure-descriptors
    • I. Gutman and B. Furtula, Hyper-Wiener index vs. Wiener index. Two highly correlated structure-descriptors, Monatshefte für Chemie 134 (2003), 975-981.
    • (2003) Monatshefte Für Chemie , vol.134 , pp. 975-981
    • Gutman, I.1    Furtula, B.2
  • 18
    • 84880115575 scopus 로고    scopus 로고
    • The Harary index of a graph under perturbation
    • C.-X. He, P. Chen and B.-F. Wu, The Harary index of a graph under perturbation, Discrete Math. Algorithms Appl. 2 (2010), no. 2, 247-255.
    • (2010) Discrete Math. Algorithms Appl , vol.2 , Issue.2 , pp. 247-255
    • He, C.-X.1    Chen, P.2    Wu, B.-F.3
  • 19
    • 84858020244 scopus 로고    scopus 로고
    • The Harary index of trees
    • A. Ilic, G. Yu and L. Feng, The Harary index of trees, Utilitas Math. 87 (2012), 21-32.
    • (2012) Utilitas Math , vol.87 , pp. 21-32
    • Ilic, A.1    Yu, G.2    Feng, L.3
  • 20
    • 0041834164 scopus 로고
    • Design of topological indices. IV. Reciprocal distance matrix, related local vertex invariants and topological indices
    • O. Ivanciuc, T.-S. Balaban and A. T. Balaban, Design of topological indices. IV. Reciprocal distance matrix, related local vertex invariants and topological indices, J. Math. Chem. 12 (1993), no. 1-4, 309-318.
    • (1993) J. Math. Chem , vol.12 , Issue.1-4 , pp. 309-318
    • Ivanciuc, O.1    Balaban, T.-S.2    Balaban, A.T.3
  • 21
    • 80051499891 scopus 로고    scopus 로고
    • Tenacity and rupture degree of permutation graphs of complete bipartite graphs
    • F. Li, Q. Ye and X. Li, Tenacity and rupture degree of permutation graphs of complete bipartite graphs, Bull. Malays. Math. Sci. Soc. (2) 34 (2011), no. 3, 423-434.
    • (2011) Bull. Malays. Math. Sci. Soc. (2) , vol.34 , Issue.3 , pp. 423-434
    • Li, F.1    Ye, Q.2    Li, X.3
  • 24
    • 0000257423 scopus 로고
    • The Wiener index: Development and applications
    • S. Nikolić and N. Trinajstić, The Wiener index: Development and applications, Croat. Chem. Acta 68 (1995), 105-129.
    • (1995) Croat. Chem. Acta , vol.68 , pp. 105-129
    • Nikolić, S.1    Trinajstić, N.2
  • 25
    • 9644276263 scopus 로고
    • On the Harary index for the characterization of chemical graphs
    • D. Plavšić, S. Nikolić, N. Trinajstić and Z. Mihalić, On the Harary index for the characterization of chemical graphs, J. Math. Chem. 12 (1993), no. 1-4, 235-250.
    • (1993) J. Math. Chem , vol.12 , Issue.1-4 , pp. 235-250
    • Plavšić, D.1    Nikolić, S.2    Trinajstić, N.3    Mihalić, Z.4
  • 26
    • 0003391553 scopus 로고
    • second edition, Mathematical Chemistry Series, CRC, Boca Raton, FL
    • N. Trinajstić, Chemical Graph Theory, second edition, Mathematical Chemistry Series, CRC, Boca Raton, FL, 1992.
    • (1992) Chemical Graph Theory
    • Trinajstić, N.1
  • 27
    • 8544254107 scopus 로고
    • Structural determination of paraffin boiling point
    • H. Wiener, Structural determination of paraffin boiling point, J. Amer. Chem. Soc. 69 (1947), 17-20.
    • (1947) J. Amer. Chem. Soc , vol.69 , pp. 17-20
    • Wiener, H.1
  • 28
    • 82755188236 scopus 로고    scopus 로고
    • Trees with the seven smallest and eight greatest Harary indices
    • K. Xu, Trees with the seven smallest and eight greatest Harary indices, Discr. Appl. Math. 160 (2012), 321-331.
    • (2012) Discr. Appl. Math , vol.160 , pp. 321-331
    • Xu, K.1
  • 29
    • 79960923804 scopus 로고    scopus 로고
    • On Harary index of graphs
    • K. Xu and K. C. Das, On Harary index of graphs, Discr. Appl. Math. 159 (2011), 1631-1640.
    • (2011) Discr. Appl. Math , vol.159 , pp. 1631-1640
    • Xu, K.1    Das, K.C.2
  • 30
    • 79952850024 scopus 로고    scopus 로고
    • Hyper-Wiener and Harary indices of graphs with cut edges
    • K. Xu and N. Trinajstić, Hyper-Wiener and Harary indices of graphs with cut edges, Util. Math. 84 (2011), 153-163.
    • (2011) Util. Math , vol.84 , pp. 153-163
    • Xu, K.1    Trinajstić, N.2
  • 31
    • 79251621265 scopus 로고    scopus 로고
    • On the maximal Harary index of a class of bicyclic graphs
    • G. Yu and L. Feng, On the maximal Harary index of a class of bicyclic graphs, Util. Math. 82 (2010), 285-292.
    • (2010) Util. Math , vol.82 , pp. 285-292
    • Yu, G.1    Feng, L.2
  • 33
    • 3843121931 scopus 로고    scopus 로고
    • Relations between Wiener, hyper-Wiener and Zagreb indices
    • B. Zhou and I. Gutman, Relations between Wiener, hyper-Wiener and Zagreb indices, Chem. Phys. Lett. 394 (2004), 93-95.
    • (2004) Chem. Phys. Lett , vol.394 , pp. 93-95
    • Zhou, B.1    Gutman, I.2
  • 34
    • 84863800453 scopus 로고    scopus 로고
    • About a conjecture on the Randić index of graphs
    • L. Zuo, About a conjecture on the Randić index of graphs, Bull. Malays. Math. Sci. Soc. (2) 35 (2012), no. 2, 411-424.
    • (2012) Bull. Malays. Math. Sci. Soc. (2) , vol.35 , Issue.2 , pp. 411-424
    • Zuo, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.