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Journal of Applied Mathematics
Volume 2012, Article ID 520156, 8 pages
http://dx.doi.org/10.1155/2012/520156
Research Article

The Merrifield-Simmons Index and Hosoya Index of 𝐢(𝑛,π‘˜,πœ†) Graphs

1Department of Mathematics, Tianjin Polytechnic University, No. 399 Binshuixi Road, Xiqing District, Tianjin 300387, China
2Department of Mathematics, Tianjin University of Science and Technology, Tianjin 300457, China

Received 29 May 2012; Revised 18 June 2012; Accepted 27 June 2012

Academic Editor: Ferenc Hartung

Copyright © 2012 Shaojun Dai and Ruihai Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. Diestel, Graph Theory, vol. 173 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2nd edition, 2000. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  2. R. E. Merrifield and H. E. Simmons, Topological Methods in Chemistry, John Wiley & Sons, New York, NY, USA, 1989.
  3. H. Hosoya, β€œTopological index, a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons,” Bulletin of the Chemical Society of Japan, vol. 44, pp. 2322–2339, 1971. View at Google Scholar
  4. H. Deng and S. Chen, β€œThe extremal unicyclic graphs with respect to Hosoya index and Merrifield-Simmons index,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 59, no. 1, pp. 171–190, 2008. View at Google Scholar Β· View at Zentralblatt MATH
  5. M. Fischermann, I. Gutman, A. Hoffmann, D. Rautenbach, D. Vidovic, and L. and Volkmann, β€œExtremal chemical trees,” Zeitschrift für Naturforschung Section B-A Journal of Chemical Sciences, vol. 57, pp. 49–52, 2002. View at Google Scholar
  6. M. Fischermann, L. Volkmann, and D. Rautenbach, β€œA note on the number of matchings and independent sets in trees,” Discrete Applied Mathematics, vol. 145, no. 3, pp. 483–489, 2005. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  7. I. Gutman, β€œExtremal hexagonal chains,” Journal of Mathematical Chemistry, vol. 12, no. 1–4, pp. 197–210, 1993. View at Publisher Β· View at Google Scholar
  8. I. Gutman and F. J. Zhang, β€œOn the ordering of graphs with respect to their matching numbers,” Discrete Applied Mathematics, vol. 15, no. 1, pp. 25–33, 1986. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  9. Y. Hou, β€œOn acyclic systems with minimal Hosoya index,” Discrete Applied Mathematics, vol. 119, no. 3, pp. 251–257, 2002. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  10. S. G. Wagner, β€œExtremal trees with respect to Hosoya index and Merrifield-Simmons index,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 57, no. 1, pp. 221–233, 2007. View at Google Scholar Β· View at Zentralblatt MATH
  11. I. Gutman and O. E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin, Germany, 1986. View at Publisher Β· View at Google Scholar
  12. J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, American Elsevier, New York, NY, USA, 1976.
  13. H. Deng, β€œThe smallest Merrifield-Simmons index of (n,n+1)-graphs,” Mathematical and Computer Modelling, vol. 49, no. 1-2, pp. 320–326, 2009. View at Publisher Β· View at Google Scholar
  14. H. Deng, β€œThe largest Hosoya index of (n,n+1)-graphs,” Computers & Mathematics with Applications, vol. 56, no. 10, pp. 2499–2506, 2008. View at Publisher Β· View at Google Scholar