Calculating the degree distance of partial Hamming graphs

Match

Volumn 63, Issue 2, 2010, Pages 411-424

  Ilić, Aleksandar ^a   Klavžar, Sandi ^b,c   Stevanović, Dragan ^d,e  

^a UNIVERSITY OF NI   (Serbia)

^b UNIVERSITY OF LJUBLJANA   (Slovenia)

^c UNIVERSITY OF MARIBOR   (Slovenia)

^d UNIVERSITY OF PRIMORSKA   (Slovenia)

^e MATHEMATICAL INSTITUTE   (Serbia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77951097294     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. A. A. Dobrynin, A. A. Kochetova, Degree distance of a graph: A degree analogue of the Wiener index, J. Chem. Inf. Comput. Sci. 34 (1994), 1082-1086.
2. I. Gutman, Selected properties of the Schultz molecular topological index, J. Chem. Inf. Comput. Sci. 34 (1994), 1087-1089.
3. A. A. Dobrynin, Explicit relation between the Wiener index and the Schultz index of catacondensed benzenoid graphs, Croat. Chem. Acta 72 (1999), 869-874.
4. H. P. Schultz, T. P. Schultz, Topological organic chemistry. 12. Whole-molecule Schultz topological indices of alkanes, J. Chem. Inf. Comput. Sci. 40 (2000), 107-112.
5. B. Zhou, Bounds for the Schultz molectdar topological index, MATCH Conunun. Math. Comput. Chem. 56 (2006), 189-194.
6. P. Dankehnann, I. Gutman, S. Mukwembi, H. C. Swart, On the degree distance of a graph. Discrete Appl. Math., in press, doi:10.1016/j.dam.2009.04. 006
7. A. A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: theory and applications. Acta Appl. Math. 66 (2001), 211-249.
8. A. A. Dobrynin, I. Gutman, S. Klavžar, P. Žigert, Wiener index of hexagonal systems. Acta Appl. Math. 72 (2002), 247-294.
9. I. Gutman, S. Klavžar, Bounds for the Schultz molecular topological index of benzenoid systems in terms of the Wiener index, J. Chem. Inf. Comput. Sci. 37 (1997), 741-744.
10. S. Klavžar, I. Gutman, A comparison of the Schultz molecular topological index with the Wiener index, J. Chem. Inf. Comput. Sci. 36 (1996), 1001-1003. (Pubitemid 126581758)
11. D. J. Klein, Z. Mihalić, D. Plavšić, N. Trinajstić, Molecular topological index: A relation with the Wiener index, J. Chem. Inf. Comput. Sci. 32 (1992), 304-305.
12. D. Plavšić, S. Nikolić, N. Trinajstić, D. J. Klein, Relation between the Wiener index and the Schultz index for several classes of chemical graphs, Croat. Chem. Acta 66 (1993), 345-353.
13. I. Tomescu, Some extremal properties of the degree distance of a graph. Discrete Appl. Math 98 (1999), 159-163.
14. I. Tomescu, Unicyclic and bicyclic graphs having minimum degree distance, Discrete Appl. Math. 156 (2008), 125-130.
15. I. Tomescu, Properties of connected graphs having minimum degree distance. Discrete Math. 309 (2009), 2745-2748.
16. O. Bucicovschi, S. M. Cioabǎ, The minimum degree distance of graphs of given order and size. Discrete Appl. Math. 156 (2008), 3518-3521.
17. H. Hua, Wiener and Schultz molecular topological indices of graphs with specified cut edges, MATCH Conunun. Math. Comput. Chem. 61 (2009), 643-651.
18. H. Deng, The Schultz Molecular Topological Index of Polyhex Nanotubes, MATCH Commun. Math. Comput. Chem. 57 (2007), 677-684.
19. 4, MATCH Commun. Math. Comput. Chem. 59 (2008), 429-435.
20. S. Klavžar, On the canonical metric representation, average distance, and partial Hamming graphs, European J. Combin. 27 (2006), 68-73.
21. W. Imrich, S. Klavžar, Product Graphs: Structure and Recognition, John Wiley & Sons, New York, 2000.
22. B. Brešar, Partial Hamming graphs and expansion procedures, Discrete Math. 237 (2001), 13-27.
23. V. Chepoi, Isometric subgraphs of Hamming graphs and d-convexity, Cybernetics 1 (1988), 6-11.
24. E. Wilkeit, Isometric embeddings in Hamming graphs, J. Combin. Theory Ser. B 50 (1990), 179-197.
25. R. L. Graham, P. M. Winkler, On isometric embeddings of graphs, Trans. Amer. Math. Soc. 288 (1985), 527-536.
26. D. Djoković, Distance preserving subgraphs of hypercubes, J. Combin. Theory Ser. B 14 (1973), 263-267.
27. P. Winkler, Isometric embeddings in products of complete graphs, Discrete Appl. Math. 7 (1984), 221-225.
28. B. Brešar, On the natural imprint function of a graph, European J. Combin. 23 (2002), 149-161.
29. M. Chastand, Fiber-complemented graphs. I. Structure and invariant subgraphs. Discrete Math. 226 (2001), 107-141.
30. W. Imrich, Embedding graphs into Cartesian products, in: Graph Theory and its Applicar tions: East and West, Ann. New York Acad. Sci. 576 (1989), 266-274.
31. M. Deza, M. Laurent, Geometry of Cuts and Metrics, Springer-Verlag, Berlin, 1997.
32. S. Klavžar, Bird's eye view of the cut method and a survey of its applications in chemical graph theory, MATCH Commun. Math. Comput. Chem. 60 (2008), 255-274.
33. S. Klavžar, I. Gutman, Wiener number of vertex-weighted graphs and a chemical application. Discrete Appl. Math. 80 (1997), 73-81.
34. V. Chepoi, On distances in benzenoid systems, J. Chem. Inf. Comput. Sci. 36 (1996), 1169-1172.
35. I. Gutman, S. Klavžar, An algorithm for the calculation of the Szeged index of benzenoid hydrocarbons, J. Chem. Inf. Comput. Sci. (35) (1995), 1011-1014.
36. V. Chepoi, S. Klavžar, The Wiener index and the Szeged index of benzenoid systems in linear time, J. Chem. Inf. Comput. Sci. 37 (1997), 752-755.
37. P. Žigert, S. Klavžar, I. Gutman, Calcxdating the hyper-Wiener index of benzenoid hydrocarbons, ACH Models Chem. 137 (2000), 83-94.
38. S. Klavžar, P. Žigert, I. Gutman, An algorithm for the calculation of the hyper-Wiener index of benzenoid hydrocarbons, Comput, Chem. 24 (2000), 229-233.
39. R. Todeschini, V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000.
40. M. V. Diudea, I. Gutman, L. Jantschi, Molecular Topology, Nova, Huntington, New York, 2001.