More on the Harary index of cacti

Journal of Applied Mathematics and Computing

Volumn 43, Issue 1-2, 2013, Pages 369-386

  Wang, Hongzhuan ^a,b   Kang, Liying ^a  

^a SHANGHAI UNIVERSITY   (China)

^b HUAIYIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Cactus; Cut edge; Extremal graph; Harary index; Pendant vertex; Perfect matching

Indexed keywords

CACTUS; CUT EDGE; EXTREMAL GRAPH; HARARY INDEX; PENDANT VERTICES; PERFECT MATCHINGS;

COMPUTATIONAL METHODS; MATHEMATICAL TECHNIQUES;

GRAPH THEORY;

EID: 84883808270     PISSN: 15985865     EISSN: None     Source Type: Journal    
DOI: 10.1007/s12190-013-0668-y     Document Type: Article

References (23)

1. Bondy, J.A.; Murty, U.S.R.: Graph Theory with Applications. Macmillan, New York (1976)
2. Bose, S.S.; Nath, M.; Paul, S.: On the distance spectral radius of cacti. Linear Algebra Appl. 437, 2128-2141 (2012)
3. Das, K.C.; Zhou, B.; Trinajstić, N.: Bounds on Harary index. J. Math. Chem. 46, 1369-1376 (2009)
4. Deng, H.Y.: Wiener indices of spiro and polyphenyl hexagonal chains. Math. Comput. Model. 55, 634-644 (2012)
5. Diudea, M.V.: Indices of reciprocal properties or Harary indices. J. Chem. Inf. Comput. Sci. 37, 292-299 (1997)
6. Estrada, E.; Rodriguez, L.: Matrix algebraic manipulation of molecular graphs, I. Harary- and MTI-like molecular descriptors. MATCH Commun. Math. Comput. Chem. 35, 157-167 (1997)
7. Feng, L.; Ilić, A.: Zagreb, Harary and hyper-Wiener indices of graphs with a given matching number. Appl. Math. Lett. 23, 943-948 (2010)
8. Gutman, I.: A property of the Wiener number and its modifications. Indian J. Chem.; Sect. A 36, 128-132 (1997)
9. Hamzeh, A.; Hossein-Zadeh, S.; Ashafi, A.R.: y-Wiener index of composite graphs. Appl. Math. Lett. 24, 1099-1104 (2011)
10. Ilić, A.; Yu, G.; Feng, L.: The Harary index of trees. Util. Math. 87, 21-32 (2012)
11. Ivanciuc, O.; Balaban, T.S.; Balaban, A.T.: Reciprocal distance matrix related local vertex invariants and topological indices. J. Math. Chem. 12, 309-318 (1993)
12. Khalifeh, M.H.; Yousefi-Azari, H.; Ashrafi, A.R.: The hyper-Wiener index of graph operations. Comput. Math. Appl. 56, 1402-1407 (2008)
13. Lučić, B.; Miličević, A.; Nikolić, S.; Trinajstić, N.: Harary index-twelve years later. Croat. Chem. Acta 75, 847-868 (2002)
14. Plavšić, D.; Nikolić, S.; Trinajstić, N.; Mihalić, Z.: On the Harary index for the characterization of chemical graphs. J. Math. Chem. 12, 235-250 (1993)
15. Wang, H.; Kang, L.: On the Harary index of cacti. Util. Math. (accepted)
16. Wiener, H.: Structural determination of paraffin boiling point. J. Am. Chem. Soc. 69, 17-20 (1947)
17. Xu, K.: Trees with the seven smallest and eight greatest Harary indices. Discrete Appl. Math. 160, 321-331 (2012)
18. Xu, K.; Das, K.C.: On Harary index of graphs. Discrete Appl. Math. 159, 1631-1640 (2011)
19. Xu, K.; Das, K.C.: Extremal unicyclic and bicyclic graphs with respect to Harary index. Bull. Malays. Math. Soc. 36(2), 373-383 (2013)
20. Xu, K.; Trinajstić, N.: Hyper-Wiener and Harary indices of graphs with cut edges. Util. Math. 84, 153-163 (2011)
21. Xu, K.; Das, K.C.; Hua, H.B.; Diudea, M.: Maximal Harary index of unicyclic graphs with given matching number. Stud. Univ. Babes-Bolyai Chem. (accepted)
22. Zhou, B.; Trinajstić, N.: On reciprocal molecular topological index. J. Math. Chem. 44, 235-243 (2008)
23. Zhou, B.; Cai, X.; Trinajstić, N.: On the Harary index. J. Math. Chem. 44, 611-618 (2008)