Authors:
K. Manimekalai,S. Manisha,P. Jagadeeswari,DOI NO:
https://doi.org/10.26782/jmcms.spl.2019.08.00073Keywords:
Square sum labeling,Cycle of Cycle graphs and H(r),Abstract
A (p ,q)-graph G(V,E) is said to be square sum if their exist a bijection g: V→{0, 1, 2, …, p -1} such that the induced map g*: E→N defined by g*(xy) = [g(x)]2 +[g(y)]2 for every xyE is one to one. The H-graph H(r) = (V,E) is 3-reqular graph with V= {vi,j: i =1, 2, 3; j = 1, 2, …,2r}and E = , 4 1 k k E where E1={𝑣,𝑣, |i =1,3 & 1j 2r-1}, E2 ={𝑣,𝑣,|1j 2r-1 & j odd}, E3 = {𝑣,𝑣,,𝑣,𝑣, }, E4={𝑣,𝑣, |i=1,2 & 1j 2r}. Here we examine the square sum labeling of Cycle of Cycle graphs Ct(Cn) for t,n≥3 and H(r).Refference:
I. Ajitha V., Arumugam S. and Germina K.A, “On square sum graphs”, AKCE
J. Graphs and Combinatorics, 6(1) pp.1-10, 2009.
II. Beineke.L.W. And S.M.Hegde, Discuss. Math. Graph Theory 21, 63, 2001.
III. Gallian, J.A. “A dynamic survey of graph labeling” The Electronic Journal of
Combinatorics, #DS6, 2017
IV. Germina.K.A and R.Sebastian “Further results on square sum graphs”
International
Mathematical Forum, Vol. 8 (1), pp. 47-57, 2013.
V. Harary F. “Graph theory” Narosa Publishing House, 2001.
VI. Kaneria V. J., Makadia H.M. , Jariya M.M., “Graceful Labeling for Cycle of
Graphs”,
International Journal of Mathematics Research, Vol. 6(2), pp. 173–178, 2014.
VII. Shiama .J, “Square sum labeling for some middle and total graphs”
International Journal of Computer Applications (0975-8887), Vol. 37(4),
January 2012.