Hamiltonian Cycle and Hamiltonian Path Decomposition of Fan Graphs

L.T. Cherin Monish Femila¹ , S. Asha²

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.2 , pp.207-211, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.207211

Online published on Apr 30, 2019

Copyright © L.T. Cherin Monish Femila, S. Asha . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

862 Views    496 Downloads    111 Downloads

Abstract :
A path in a graph G that contains every vertex of G is called Hamiltonian path. A cycle in a graph G that contains every vertex of G is called a Hamiltonian cycle of G. A Hamiltonian graph is a graph that contains a Hamiltonian cycle. A graph is uniquely Hamiltonian if it contains exactly one Hamiltonian cycle. A decomposition of a graph G into Hamiltonian cycles will be called Hamiltonian decomposition of G. In this paper, we investigate Hamiltonian path decomposition of fan graph. Using this concept, we also investigate Hamiltonian decomposition of double fan graph.

Key-Words / Index Term :
Hamiltonian cycle, Hamiltonian graph, uniquely Hamiltonian, Hamiltonian decomposition, fan graph.

References :
[1] Klas Markstrom, “Even cycle decomposition of 4-regular graphs and line graphs”.
[2] Murugesan N., Vanadhi T., “Hamiltonian decomposition of complete graphs and complete digraphs”, Global Journal of theoretical and applied Mathematics Sciences, Vol 1, No 1, (2011), ISSN 2248-9916.
[3] Bermond J.C., “ Hamiltonian Decompositions of Graphs, Directed Graphs and Hypergraphs”, Advances in Graph Theory, Annals of Discrete Mathematics 3 (1978) 21-28.
[4] Ali Ahmad, Ruxandra Marinescu-Ghemeci, “Radio Labeling of Some Ladder-Related Graphs”, MATH. REPORTS 19 (69), 1 (2017), 107-119.
[5] Bondy J.A., Murty U.S.R., “Graph Theory with Applications”, 1976, Elsevier, New York.
[6] Bosak J., “Decompositions of Graphs”, 1990, Kluwer Academic Press, Dordrecht.
[7] Cherin Monish Femila L.T., Asha S., “Hamiltonian Decomposition of Special Class of Ladder Graphs”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Volume-5, Issue-5, pp.114-120, October (2018), E-ISSN: 2348-4519.
[8] Cherin Monish Femila L.T., Asha S., “Hamiltonian Decomposition of Wheel Related Graphs”, International Journal of Scientific Research and Review, ISSN NO: 2279-543X.