Some Edge Cut Sets and an Upper bound for Edge Tenacity of Organic Compounds CnH2n+2

Document Type : Research Paper


1 University of Qom

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


The graphs play an important role in our daily life. For example, the urban transport network can be represented by a graph, as the intersections are the vertices and the streets are the edges of the graph. Suppose that some edges of the graph are removed, the question arises, how damaged the graph is. There are some criteria for measuring the vulnerability of graph; the tenacity is the best criteria for measuring it. In this paper, we find some edge cut sets for organic compounds CnH2n+2 and obtain an upper bound for Te(CnH2n+2) by these edge cut sets. 


  1. J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, The Macmillan Press Ltd., (1976).
  2. F. Li, Some results on Tenacity of Graphs, WSEAS Transactions on Mathematics, 11: 760–772, (2012).
  3. T.C.E. Cheng, Yin-Kui Li, Chuan-Dong Xu, and Sheng-Gui Zhang, Extrem Tenacity of graphs with given order and size, J. Oper. Res. Soc. China, 2: 307–315, (2014).
  4. D. Moazzami and B. Salehian, On the edge-Tenacity of graphs, Int. Math, Forum, 3: 929–936, (2008).
  5. L.L. Doty and K.K. Ferland, Some maximally tough circulants, Ars. Combin., 87: 193–203, (2008).
  6. K.K. Feraland, Maximum toughness among (n,m)graphs, J. Combin. Math. Combin. Comput., 43: 43–55, (2002).
  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. W.D. Goddard and H. C. Swart, On some extremal problems in connectivity, Graph Theory Combin. App., 1: 535–551, (1991).
  9. D. Moazzami, Stability measure of a graph: A survy, Util. Math., 57: 171–191, (2000).
  10. L.L. Doty and K.K. Ferland, Supertough graphs, OR Spektrum, 13: 147–151, (1991).
  11. Z-P Wang, G. Ren, and L-c. Zhao, Edge-Tenacity in graphs, J. Math. Res. Exposition, 24: 405–410, (2004).
  12. Y. Wu and X.S. Wei, Edge-teancity of graphs, Gongcheng Shuxue Xue- Bao, 21: 704– 708, (2004).