Some Results on Graceful Labeling for families of Plus Graph

V J Kaneria; H M Makadia

V J Kaneria Department of Mathematics, Saurashtra University, Rajkot-360005, India.
H M Makadia Government Engineering College, Rajkot-360005, India.

Keywords: Graceful labeling, open star of graph, one point union of path graphs, path union, plus graph, cycle with twin chords

Abstract

In this paper we investigated some Plus graph P ln related families with their graceful labeling. We obtained graceful labeling for open star of plus graph S(t · P ln) and one point union for path of plus graph Pnt(tn · P lm). We also obtained graceful labeling of cycle Cm (m ≡ 0 (mod 4)) and plus graph with a path of arbitrary length and by joining Cm+ (m ≡ 2 (mod 4)), a cycle with twin chords and P ln with a path of arbitrary length.

References

A. Rosa, On certain valuation of graph, Theory of Graphs (Rome, July 1966), Goden and Breach, N. Y. and Paris, (1967), 349-355.

S.W.Golomb, How to number a graph, Graph Theory and Computing (R. C. Read. Ed.) Academic Press, New York, (1972), 23-37.

V.J.Kaneria and H.M.Makadia, Graceful Labeling for plus graph, International Journal of Current Research in Science and Technology, 1(3)(2015), 15-20.

V.J.Kaneria, Meera Meghpara and H.M.Makadia, Graceful labeling for Open Star of graphs, Int. J. of Math. and Stat. Inve., 2(9)(2014), 19-23.

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., 2(5)(2014), 470-472.

V.J.Kaneria and M.M.Jariya, Smooth graceful graphs and its applications to construct graceful graphs, Int. J. of Sci. and Res., 3(8)(2014), 909-912.

F.Harary, Graph theory, Addition Wesley, Massachusetts, (1972).

J.A.Gallian, A Dynamic Survey of Graph Labeling, The Electronics Journal of Combinatorics, 17(2014), #DS6.