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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 51 | Number 6 | Year 2017 | Article Id. IJMTT-V51P552 | DOI : https://doi.org/10.14445/22315373/IJMTT-V51P552

Graceful Labeling of Quarilateral Snakes


G. Sankari, S. Lavanya
Abstract

The graceful labeling of a graph G with q edges means that there is an injection g : V(G) to { 0,1, 2, ..., q} such that, when each edge uv is assigned the label |g(u)-g(v)|, the resulting edge labels are {1, 2, 3, ...q}. A graph which admits an graceful labeling is called an graceful graph. In this paper we will prove alternate quadrilateral snakes A(QSn), double quadrilateral snakes D(QSn), double alternate quadrilateral snakes DA(QSn) are graceful.

Keywords
alternate quadrilateral snakes, double quadrilateral snakes, double alternate quadrilateral snakes, graceful labeling.
References

[1] Barrientos C., 'Graceful labelings of cyclic snakes' ,Ars Combin., 60, 85-99 (2001).
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[3] Gallian Joseph A. 'The electronic Journal of Combinatorics', A Dynamic survey of graph labeling (2016).
[4] Gnanajothi R.B., 'Topics in graph theory', Ph.D.Thesis, Madurai Kamaraj University (1991).
[5] Golomb S.W., 'How to number a graph in graph Theory and computing', R.C. Read, ed., Academic Press, New York, 23-37 (1972).
[6] Murthy, U.S.R and Bondy, J.A., 'Graph theory with applications' Elsevier North-Holland (1976).
[7] Rosa A.,'On certain valuations of the vertices of a graph', Theory of graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N.Y. and Dunod Paris, Vol.349-355 (1967).
[8] Rosa A., 'Cyclic Steiner Triple System and Labelings of Triangular Cacti', Scientia, 1, pp.87-95 (1988).

Citation :

G. Sankari, S. Lavanya, "Graceful Labeling of Quarilateral Snakes," International Journal of Mathematics Trends and Technology (IJMTT), vol. 51, no. 6, pp. 377-380, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V51P552

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