Vertex-Cut Sets and Tenacity of Organic Compounds CnH2n+2

Document Type : Research Paper

Authors

1 University of Qom

2 Department of Mathematics, University of Qom, Qom, IRAN.

Abstract

Consider some vertices of a graph G are omitted, there are some criteria for measuring the vulnerability of the graph; Tenacity is one of them. In the definition of tenacity we use vertex cut S and some items, τ (G − S) and ω(G − S), such that τ (G − S) is the number of vertices in the largest component of G − S and ω(G − S) is the number of components of G − S. In this paper we work on tenacity of organic compound CnH2n+2. The graph of this molecule is a tree. We try on tenacity of it by the definition of the tenacity. 

Keywords

References

  1. J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, The Macmillan Press Ltd., (1976).
  2. D. Moazzami, Tenacity of a graph with maximum connectivity, J. Discrete Appl. Math., 159: 367–380, (2011).
  3. A. Mamut and E. Vumar, Vertex vulnerability parameters of Kronecker products of complete graphs, Inform. Process. Lett., 106: 258–262, (2008).
  4. D. Moazzami and B. Salehian, On the edge-tenacity of graphs, Int. Math, Forum, 3: 929–936, (2008).
  5. V. Aytac, Compuing the tenacity of some graphs, Seluk J. Appl. Math., 10: 107–120, (2009).
  6. M.B. Cozzens, D. Moazzami, and S. Stueckle, The tenacity of a graph, Graph Theory, Combinatorics, and Algorithms, Wiley-Intersci. Publ., Wiley, New York, 1(2): 1111–1112, (1995).
  7. Y-K. Li, S-g. Zhang, X-L. Li, and Y. Wu, Relationships between tenacity and some other vulnerability parameters, Basic Sci. J. Text. Univ., 17: 1–4, (2004).
  8. D. Moazzami, Vulnerability in Graphs –a comparative survey, J. Combin. Math. Combin. Comput., 30: 23–31, (1999).
  9. D. Moazzami, Stability measure of a graph: A survy, Util. Math., 57: 171–191, (2000).
  10. D. Moazzami and S. Salehian, Some results related to the tenacity and existencs of k-trees, Discrete Appl. Math., 157: 1794–1798, (2009).
  11. M.B. Cozzens, D. Moazzami, and S. Stueckle, The tenacity of the Harary graphs, J. Combin. Math. Combin. Comput., 16: 33–56, (1994).
  12. Z-P Wang, G. Ren, and L-c. Zhao, Edge-Tenacity in graphs, J. Math. Res. Exposition, 24: 405–410, (2004).
  13. Y. Wu and X.S. Wei, Edge-teancity of graphs, Gongcheng Shuxue Xue- Bao, 21: 704– 708, (2004).
Global Analysis and Discrete Mathematics
Volume 5, Issue 1
June 2020
Pages 29-50

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History

  • Receive Date: 09 July 2019
  • Accept Date: 30 May 2020

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