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Abstract
A simple connected graph G is Hamiltonian Laceable, if there exists a Hamiltonian path between every pair of distinct vertices at an odd distance in it. G is a Hamiltonian-t-laceable (t*-laceable) if there exists a Hamiltonian path in G between every pair (at least one pair) of vertices u and v in G with the property d(u,v)=t , 1≤t≤diam G. In this paper we explore Hamiltonian laceability properties of the Total graph of the Sunlet graph, Star graph, Path graph and Cycle.
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References
T. Hamada, T. Nonaka and I. Yoshimura, On the Connectivity of total graphs, Math. Ann. 196 (1972) 30-38.
D.A.Holton, Dingjun Lou and K. L. McAvaney, n-Extendibility of Line Graphs, Power Graphs and Total
Graphs, Australasian Journal of Combinatorics 11(1995), pp.215-222.
Abolfazl Tehranian and Hamid Reza Maimani, A Study of the Total Graph, International Journal of
Mathematical Sciences and Informatics, Vol. 6, No. 2(2011), pp-75-80.
Girisha. A, H. Mariswamy, Murali. R amd G. Rajendra, Hamiltonian Laceability in a Class of 4- Regular
Graphs, IOSR journal of Mathemat ics, ISSN:2278-5728, Volume 4, Issue 1 (Nov.-Dec.2012), pp. 07-12.
Leena N. shenoy and R. Murali, Laceability On a Class of Regular Graphs, International Journal of
Computational Science and Mathematics, Volume 2,Number 3 (2010),pp 397-406.
Girisha. A and R. Murali, i-Hamiltonian Laceability in Product Graphs, International Journal of
Computational Science and Mathematics, ISSN 0974-3189, Volume 4,Number 2 (2012),pp 145-158.
Girisha. A and R. Murali, Hamiltonian Laceabilityin Some Classes of the Star Graphs, ISSN:2319-5967, IJESIT,
Volume 2, Issue 3, May 2013.
Manjunath. G and R.Murali, Hamiltonian Laceability in the Brick Product C(2n+1,1,r),Advances in Applied
Mathematical Biosciences, ISSN 2248-9983, Volume 5, No.1(2014).pp.13-32.
Manjunath. G and R.Murali, Hamiltonian-t*- Laceability in Jump Graphs Of Diameter Two, IOSR Journal of
Mathematics, e-2278-3008, p-ISSn:2319-7676. Volume 10, Issue 3 Ver.III(May-Jun.2014),pp 55-63.
Manjunath. G, R.Murali and S. N. Thimmaraju, Hamiltonian Laceability in the Modified Brick Product of Odd
Cycles, International Journal of Mathemat ical Science (IJMS), Submitted.
Manjunath. G, R.Murali and Girisha. A, Hamiltonian Laceability in Line Graphs, International Journal of
Computer Applications (IJCA),0975-8887, volume 98 No.2, July 2014.