Some Results on Graceful Labeling for Step
Grid Related Graphs

H M Makadia

doi:https://doi.org/10.14445/22315373/IJMTT-V65I11P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 11 | Year 2019 | Article Id. IJMTT-V65I11P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I11P503

Some Results on Graceful Labeling for Step Grid Related Graphs

H M Makadia

Abstract

In this paper we investigated some Step Grid Stn related families with their graceful labeling. We obtained graceful labeling for t-super subdivision of the step grid graph, open star of step grid graph S(t . Stn) and one point union for path of step grid graph Pn t(tn . Stm). We also obtained graceful labeling for path union of cycle Cm (m ≡ 0 (mod 4)) with step grid graph.

Keywords

Graceful labeling, t-super subdivision of graph, open star of graph, one point union of path graphs, path union, step grid graph.

References

[1] A. Rosa, On certain valuation of graph, Theory of Graphs (Rome, July 1966), Goden and Breach, N. Y. and Paris, (1967) pp. 349-355.
[2] S. W. Golomb, How to number a graph. In: Graph Theory and Computing (R. C. Read. Ed.) Academic Press. New York, (1972) pp. 23-37.
[3] V. J. Kaneria and H. M. Makadia, Graceful Labeling for Step Grid Graph, J. of Adv. in Maths. Vol-9 (5), Nov. 2014, pp. 2647 - 2654.
[4] V. J. Kaneria, Meera Meghpara and H. M. Makadia, Graceful labeling for Open Star of graphs, Int. J. of Math. and Stat. Inve. www.ijmsi.org, vol-2(9), (2014) pp. 19-23.
[5] V. J. Kaneria and H. M. Makadia, Graceful Labeling for tensor product ot two path of odd lengths and some grid related graphs, Int. J. of Inn. in Sci. and Math. vol-2(5),(2014) pp. 470 - 472.
[6] F. Harary, Graph theory Addition Wesley, Massachusetts, 1972.
[7] J. A. Gallian, The Electronics Journal of Combinatorics, 19, ]DS6(2013).

Citation :

H M Makadia, "Some Results on Graceful Labeling for Step Grid Related Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 11, pp. 29-38, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I11P503