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DNA Computing Models.Springer. 2008. Domination in Permutation Graphs


Author(s): J.Chithra , S.P.Subbiah,V.Swaminathan
Affiliation: Department of Mathematics, Lady Doak College, Madurai, India
Year of Publication: 2014
Source: International Journal of Computing Algorithm
     
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Citation: J.Chithra, S.P.Subbiah,V.Swaminathan. "DNA Computing Models.Springer. 2008. Domination in Permutation Graphs." International Journal of Computing Algorithm 3.1 (2014): 61-64.

Abstract:
If i, j belongs to a permutation on n symbols {1, 2, …, p} and i is less than j then there is an edge between i and j in the permutation graph if i appears after j. (i. e) inverse of i is greater than the inverse of j. So the line of i crosses the line of j in the permutation. So there is a one to one correspondence between crossing of lines in the permutation and the edges of the corresponding permutation graph. In this paper we found the conditions for a permutation to realize paths and cycles and also derived the domination number of permutation graph through the permutation. AMS Subject Classification (2010): 05C35, 05C69, 20B30.


Keywords Permutation Graphs, Domination Number of a Permutation


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@article{DNA1458766, author = {J.Chithra,S.P.Subbiah,V.Swaminathan}, title = {DNA Computing Models.Springer. 2008. Domination in Permutation Graphs}, journal={International Journal of Computing Algorithm}, volume={3}, issue={1}, issn = {2278-2397}, year = {2014}, publisher = {Scholarly Citation Index Analytics-SCIA}

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  • [2] R.Adin and Y.Roichman, On Degrees in the Hasse Diagram of the Strong Bruhat Order, Seminaire Lotharingien d Combinatoire 53 (2006), B53g.
  • [3] Charles J. Colbourn , Lorna K.Stewart “Permutation Graphs: Connected Domination and Steiner Trees”, Research Report CS-85-02, Canada, 1985.
  • [4] Frank Harary, Graph Theory, Narosa Publishing House, Calcutta, pp. 2001.
  • [5] Teresa W.Haynes, Stephen T. Hedetneimi, PeterJ.Slater, Fundamentals of Domination in Graphs, in Graphs, Marcel Dekker,INC.,New York,pp.1-106, 1998.
  • [6] Ryuhei Uehara, Gabriel Valiente, Linear structure of Bipartite Permutation Graphs and the Longest Path Problem, 2006.
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