APPLICATION OF LINE GRAPHS AND COMPLETE HAMILTONIAN GRAPHS
Abstract
In 1856, Hamiltonian introduced the Hamiltonian Graph where a Graph which is covered all the vertices without repetition and end with starting vertex. In this Paper I would like to prove that Let “G” be a Complete graph with at least four vertices. Then, the line graph “L(G)” is Complete Hamiltonian if and only if “G” is dominating trailable.
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References
Bondy J.A. and V. Chvátal, A Method in Graph Theory, Discr. Math. 15 1976), pp 111-136.
Dirac G.A., Some Theorems on Abstract Graphs, Proc. Lond. Math. Soc. 2 (1952), pp 69-81.
Garey M.R and D.S. Jhonson, Computers and Intractability: A Guide to the Theory of NPCompleteness, W.H. Freeman and Company, New York.
O. Ore, Note on Hamiltonian Circuits, Am. Mat. Monthly 67 (1960), pp 55.
West D.B, Introduction to Graph Theory, Prentice-Hall, Inc., New Jersey.
Williams –Nash, C.St.J.A. “Hamiltonian Arcs and Circuits” in recent trends in graph theory ed. By M. Capobianco et al., Springer –verlag, Berlin, 1971.
V.Chvatal “New directions in Hamiltonian Graph theory” In New directions in graph theory ed. By F.Harary, Academic press, N.Y.London, 1973.
Venu Madhava Sarma.S and T.V. Pradeep Kumar International Journal of Mathematical Archive-2(12), 2011, Page 2538-2542.
Venu Madhava Sarma.S International Journal of Computer Application, Issue 2, Volume 1(February 2012) , Page 21-31.
Venu Madhava Sarma.S and T.V.Pradeep Kumar International J. of Math. Sci. & Engg. Appls. (IJMSEA) ISSN 0973-9424, Vol. 6 No. III (May 2012), pp. 47-54
Venu Madhava Sarma.S and T.V.Pradeep Kumar proceedings of Two Day UGC National seminar on “Modern Trends in Mathematics and Physical Sciences ( NSMTMPS –2012) dated 20th, 21st Jan, 2012.
D. P. Geller, The square root of a digraph, J. Combinatorial Theory, 5 (1968),320-321.
F. Harary, Graph Theory, Addison-Wesley, Reading, Mass., 1969.
A. Mukhopadhyay,The square root of a graph, J. Combinatorial Theory, 2 (1967),290-295.
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