skip to main content
10.1145/3208788.3208790acmotherconferencesArticle/Chapter ViewAbstractPublication PagesicmaiConference Proceedingsconference-collections
research-article

The Merrifield-Simmons index of two classes of lexicographic product graphs of corona graphs

Published:20 April 2018Publication History

ABSTRACT

The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph. This paper mainly discussed the Merrifield- Simmons index of two classes of lexicographic product graphs of Corona graphs P(m)n [H] and C(m)n[H], with the specific expressions are given.

References

  1. Merrifield R E, Simmons H E. Topological Methods in Chemistry{M}. New York: Wiley, 1989.Google ScholarGoogle Scholar
  2. Gutman I, Polansky O E. Mathematical Concepts in Organic Chemistry{M}. Berlin: Springer, 1986.Google ScholarGoogle Scholar
  3. Gutman I, Cyvin S J. Introduction to the Theory of Benzenoid Hydrocarbons{M}. Berlin: Springer, 1989.Google ScholarGoogle Scholar
  4. Belyĭ S B, Rovenskiĭ E A. Fibonacci numbers of graphs{J}. Journal of Combinatorial Theory, 1989, 8(2):191--209.Google ScholarGoogle Scholar
  5. Wagner S, Gutman I. Maxima and minima of the Hosoya Index and the Merrifield-Simmons index{J}. Acta Appl Math. 2010, 112:323--346. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Reyhani M H, Alikhani S, Iranmanesh M A. Hosoya and Merrifield-Simmons indices of some classes of Corona of two graphs{J}. Transactions on Combinatorics, 2012, 1(4): 1--7.Google ScholarGoogle Scholar
  7. Tian Wen Wen. The Merrifield-Simmons index and Hosoya index of some graph {D}. Lanzhou: Northwest University for Nationalities, 2014.Google ScholarGoogle Scholar
  8. Li Xia li, Ren Hai Zheng. The Hosoya index and Merrifield-Simmons index of the Vertebrated graph{J}. Journal of Northeast Normal University(Natural Science Edition), 2013, 45(1):31--34.Google ScholarGoogle Scholar
  9. Bondy J A, Murty U S R. Graph theory with applications{M}. New York: Macmillan, 1976. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Frucht R, Harary F. On the Corona of Two Graphs{J}. Aequationes Math, 1970, (4):322--325.Google ScholarGoogle ScholarCross RefCross Ref
  11. Tian Shuang Liang. Vertex-distinguishing edge colorings of the Mycielski's graphs of some lexicographic product graphs {J}. Journal of Shandong University (Natural Science), 2012, 47(8):7--10.Google ScholarGoogle Scholar

Index Terms

  1. The Merrifield-Simmons index of two classes of lexicographic product graphs of corona graphs

    Recommendations

    Comments

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Sign in
    • Published in

      cover image ACM Other conferences
      ICMAI '18: Proceedings of 2018 International Conference on Mathematics and Artificial Intelligence
      April 2018
      95 pages
      ISBN:9781450364201
      DOI:10.1145/3208788

      Copyright © 2018 ACM

      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 20 April 2018

      Permissions

      Request permissions about this article.

      Request Permissions

      Check for updates

      Qualifiers

      • research-article
    • Article Metrics

      • Downloads (Last 12 months)3
      • Downloads (Last 6 weeks)0

      Other Metrics

    PDF Format

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader