Ordering unicyclic graphs with respect to hosoya indices and Merrifield-Simmons indices

Match

Volumn 59, Issue 1, 2008, Pages 191-202

  Ye, Yali ^a   Pan, Xiang Feng ^b   Liu, Huiqing ^a  

^a HUBEI UNIVERSITY   (China)

^b ANHUI UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 42149087660     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, MacMillan, New York, 1976.
2. O. Chan, I. Gutman, T.K. Lam and R. Merris, Algebraic connections between topological indices, J. Chem. Inform. Comput. Sci., 38(1998) 62-65.
3. S.J. Cyvin and I. Gutman, Hosoya index of fused molecules, MATCH Commun. Math. Comput. Chem., 23(1988) 89-94.
4. S.J. Cyvin, I. Gutman and N. Kolakovic, Hosoya index of some polymers, MATCH Commun. Math. Comput. Chem., 24(1989) 105-117.
5. I. Gutman, Independent vertex sets in some compound graphs, Publ. Inst. Math. (Beograd), 52(1992) 5-9.
6. I. Gutman, Fragmentation formulas for the number of Kekulé structures, Hosoya and Merrifield-Simmons indices and related graph invariants, Coll. Sci. Pap. Fac. Sci. Kragujevac, 11(1990) 11-18.
7. I. Gutman, Topological properties of benzenoid systems. Merrifield-Simmons indices and independence polynomials of unbranched catafusenes, Rev. Roum. Chim., 36(1991) 379-388.
8. I. Gutman, Independent vertex sets in some compound graphs, Publ. Inst. Math. (Beograd), 52(1992) 5-9.
9. I. Gutman, H. Hosoya, G. Uraković and L. Ristić, Two variants of the topological index and the relations between them, Bull. Chem. Soc. Jpn, 65(1992) 14-18.
10. I. Gutman, N. Kolaković, Hosoya index of the second kind of molecules containing a polyacene fragment, Bull. Acad. Serbe Sci. Arts (Cl. Math. Natur.), 102(1990) 39-46.
11. I. Gutman, Extremal hexagonal chains, J. Math. Chem., 12(1993) 197-210.
12. I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin, 1986.
13. H. Hosoya, Topological index, a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Jpn., 44(1971) 2332-2339.
14. X. Li, Z.M. Li and L.S. Wang, The inverse problems for some topological indices in combinatorial chemistry, J. Comput. Biol., 10(2003) 47-55.
15. X. Li, H. Zhao and I. Gutman, On the Merrifield-Simmons index of trees, MATCH Commun. Math. Comput. Chem., 54(2005) 389-402.
16. X. Li and H.X. Zhao, On the Fibonacci numbers of trees, Fibonacci Quarterly, 44(2006) 32-38.
17. S. B. Lin and C. Lin, Trees and forests with large and small independent indices, Chinese J. Math., 23(3)(1995) 199-210.
18. H.-Q. Liu and M. Lu, A unified approach to extremal cacti for different indices, MATCH Commun. Math. Comput. Chem., 58(2007) 193-204.
19. H.-Q. Liu, X. Yan and Z. Yan, On the Merrifield-Simmons indices and Hosoya indices of trees with a prescribed diameter, MATCH Commun. Math. Comput. Chem., 57(2007) 371-384.
20. R.E. Merrifield and H. E. Simmons, Enumeration of structure-sensitive graphical subsets: Theory, Proc. Natl. Acad. Sci. USA, 78(1981) 692-695.
21. R.E. Merrifield and H.E. Simmons, Enumeration of structure-sensitive graphical subsets: Calculations, Proc. Natl. Acad. Sci. USA, 78(1981) 1329-1332.
22. R.E. Merrifield and H.E. Simmons, Topological Methods in Chemistry, Wiley, New York, 1989.
23. J. Ou, On extremal unicyclic molecular graphs with prescribed girth and minimal Hosoya index, J. Math. Chem., DOI: 10.1007/s10910-006-9112-y.
24. X.-F. Pan, J.-M. Xu, C. Yang and M.-J. Zhou, Some graphs with minimum Hosoya index and maximum Merrifield-Simmons index, MATCH Commun. Math. Comput. Chem., 57(2007) 235-242.
25. H. Prodinger, R. F. Tichy, Fibonacci numbers of graphs, Fibonacci Quart, 20(1982) 16-21.
26. L. Türker, Contemplation on the Hosoya indices, J. Mol. Struct. (Theochem), 623(2003) 75-77.
27. A.-M. Yu and F. Tian, A kind of graphs with minimal Hosoya indices and maximal Merrifield-Simmons indices, MATCH Commun. Math. Comput. Chem., 55(2006) 103-118.
28. L.-Z. Zhang and F. Tian, Extremal catacondensed benzenoids, J. Math. Chem., 34(2003) 111-122.