Research Article
A Result on Line Graphs and Hamiltonian Graphs
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 119 - Issue 4 |
| Published: June 2015 |
| Authors: S.Venu Madhava Sarma, T.Ravi Kumar, T.V.Pradeep Kumar |
10.5120/21055-3703
|
S.Venu Madhava Sarma, T.Ravi Kumar, T.V.Pradeep Kumar . A Result on Line Graphs and Hamiltonian Graphs. International Journal of Computer Applications. 119, 4 (June 2015), 16-19. DOI=10.5120/21055-3703
@article{ 10.5120/21055-3703,
author = { S.Venu Madhava Sarma,T.Ravi Kumar,T.V.Pradeep Kumar },
title = { A Result on Line Graphs and Hamiltonian Graphs },
journal = { International Journal of Computer Applications },
year = { 2015 },
volume = { 119 },
number = { 4 },
pages = { 16-19 },
doi = { 10.5120/21055-3703 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2015
%A S.Venu Madhava Sarma
%A T.Ravi Kumar
%A T.V.Pradeep Kumar
%T A Result on Line Graphs and Hamiltonian Graphs%T
%J International Journal of Computer Applications
%V 119
%N 4
%P 16-19
%R 10.5120/21055-3703
%I Foundation of Computer Science (FCS), NY, USA
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 If 'G' is a Complete and locally Complete graph, on n ? 3 vertices, which does not contain an induced K1,3, then G is Hamiltonian.
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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