The extremal unicyclic graphs with respect to Hosoya index and Merrifield-Simmons index

Match

Volumn 59, Issue 1, 2008, Pages 171-190

  Deng, Hanyuan ^a   Chen, Shubo ^b  

^a HUNAN NORMAL UNIVERSITY   (China)

^b HUNAN CITY UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 42149182933     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. 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.
2. H. Hosoya, Topological index as a common tool for quantum chemistry, statistical mechanics, and graph theory. In Mathematical and computational concepts in chemistry (Dubrovnik, 1985), Ellis Horwood Ser. Math. Appl., pages 110-123. Horwood, Chichester, 1986.
3. R. E. Merrifield and H. E. Simmons, Topological methods in chemistry, Wiley, New York, 1989.
4. I. Gutman and O. E. Polansky, Mathematical concepts in organic chemistry, Springer- Verlag, Berlin, 1986.
5. N. Trinajstić, Chemical graph theory, CRC Press, Boca Raton, FL., 1992.
6. M. Fischermann, I. Gutman, A. Hoffmann, D. Rautcnbach, D. Vidovic, and L. Volkmann, Extremal chemical trees. Z. Naturforsch., 57a(2002)49-52.
7. Y. Hou, On acyclic systems with minimal Hosoya index, Discrete Appl. Math., 119(2002)251-257.
8. X. Li and H. Zhao, On the Fibonacci Numbers of trees, Fibonacci Quart., 44(2006)32-38.
9. X. Li, H. Zhao and I. Gutman, On the Merrifield-Simmons index of trees, MATCH Commun. Math. Comput. Chem, 54(2005)389-402.
10. S. B. Lin and C. Lin, Trees and forests with large and small independent indices, Chinese J. Math., 23(1995)199-210.
11. A. 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.
12. L. Z. Zhang, The proof of Gutman's conjectures concerning extremal hexagonal chains, J. Systems Sci. Math. Sci, 18(1998)460-465.
13. M. Fischermann, L. Volkmann, and D. Rautenbach, A note on the number of matchings and independent sets in trees, Discrete Appl. Math., 145(2005)483-489.
14. I. Gutman, F. Zhang, On the ordering of graphs with respect to their matching numbers, Discrete Appl. Math. 15(1986)25-33.
15. L. Zhang, F. Tian, Extremal catacondensed benzenoids, J. Math. Chem. 34 (2003)111-122.
16. A. S. Pedersen, P. D. Vestergaard, The number of independent sets in unicyclic graphs, Discrete App. Math. 152(2005)246-256.
17. S. Wagner, Extremal trees with respect to Hosoya index and Merrifield-Simmons index, MATCH Commun. Math. Comput. Chem., 57(2007)221-233.
18. H. Li, On minimal energy ordering of acyclic conjugated molecules, J. Math. Chem. 25(1999)145-169.
19. L. Zhang, F. Tian, Extremal catacondensed benzenoids, J. Math. Chem. 34(2003)111-122.
20. H. Deng, The smallest Hosoya index in (n,n+1)-graphs, accepted by J. Math. Chem. DOI: 10.1007/s10910-006-9186-6
21. H. Deng, S. Chen, J. Zhang, The Merrifield-Simmons index in (n,n+1)-graphs, accepted by J. Math. Chem. DOI:10.1007/s10910-006-9180-z
22. H. Liu, X. Yan, 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.
23. X. Pan, C. Yang, M. J. Zhou, Some graphs with minimum Hosoya index and maximum Merrifield-Simmons index, MATCH Commun. Math. Comput. Chem. 57(2007)235-242.
24. C. Ye, J. Wang, H. Zhao, Trees with m-matchings and the third minimal Hosoya index, MATCH Commun. Math. Comput. Chem. 56(2006)593-604.
25. Z. Zhang, Merrifield-Simmons index of generalized Aztec diamonds and related graphs, MATCH Commun. Math. Comput. Chem. 56(2006)625-636.
26. H. Zhao, R. Liu, On the Merrifield-Simmons index of graphs, MATCH Commun. Math. Comput. Chem. 56(2006)617-624.