## Control Systems and Computers, N5, 2016, Article 4

##### DOI: https://doi.org/10.15407/usim.2016.05.032

*Upr. sist. maš., 2016, Issue 5 (265), pp. 32-36.
*

UDC 519.17

**Sherman **Zoya A., PhD student, V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Glushkov ave., 40, Kyiv, 03187, Ukraine, E-mail: sherman.zoya@gmail.com

### Square Sum Labeling of Some Graphs

**Introduction**. Research studies conducted by Ajitha and colleagues in the field of number theory inspired them to create two new types of labeling: square sum labeling and square difference labeling. For the first time square sum labeling was introduced to the scientific world in 2009. Its authors proved the existence of this labeling for such classes of graphs as trees, paths, cycles, complete graphs Kn (for n ≤ 5), lattices, one-point union of n copies of the cycle Cn. Germina and Sebastian identified new

classes of graphs that had square sum labeling, such as: Unicycle graphs, mCn, cycle with a chord, the graph defined by path union of k copies of Cn. In 2012, Somashekara and Veena used the term “square sum labeling” in the meaning “strongly square sum labeling”. They proved that paths, disjoint union of stars, complete n-ary trees and lobsters had strongly square sum labeling. These labelings, as well as majority of others, are well presented in the review published by Gallian.

**Results**. The existence of square sum labeling for new types of graphs, which were obtained using: i) one-point union of any square sum graph with the path, ii) edge union of n copies of the cycle C3 with the path; iii) path union of cycles is proved. In addition, the total graph of the path and disjoint union of two square sum graphs are square sum graphs is shown.

**Download full text! (In Russian).**

**Keywords**: Square sum labeling, square sum graph, total graph.

1. Ajitha, V., Princy, K., Lokesha, V. et al., 2012. ” On square difference Graphs”. Int. J. of Mathematical Combinatorics, 1(1), pp. 31–40.

2. Germina, K., Sebastian, R., 2013. “On square sum graphs”. Proyecciones, 2 (32), pp. 107–117.

https://doi.org/10.4067/S0716-09172013000200002

3. Somashekara, D.D., Veena, C.R., 2012. “On square sum labelings of graphs”. Proc. Jangjeon Math. Soc., 15(1), pp. 69–78.

4. Gallian, J.A., 2014. “A dynamic survey of graph labeling”. The Electronic j. of Combinatorics, DS6, pp. 1–84.

5. Harary, F., 1973. “Graph Theory”. Reading, Massachusetts: Addison Wesley, pp. 1–384.

**Received **19.10.2016