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## Proyecciones (Antofagasta)

##
*Print version* ISSN 0716-0917

### Proyecciones (Antofagasta) vol.34 no.1 Antofagasta Mar. 2015

#### http://dx.doi.org/10.4067/S0716-09172015000100005

**Square Sum Labeling of Class of Planar Graphs**

**Reena Sebastian **

S. E. S. College, India

**K. A. Germina**

Central University of Kerala, India

**ABSTRACT**

A (p, q) graph G is said to be square sum, if there exists a bijection f : V(G) → {0,1, 2,...,p — 1} such that the induced function f * : E(G)→ N defined by f ^{*} (uv) = (f (u))^{2} + (f (v))^{2}, ∀ uv ∈ E(G) is injective. In this paper we proved that the planar graphs Pl_{m},_{n},TBL(n,α,k,β) and higher order level joined planar grid admits square sum labeling. Also the square sum properties of several classes of graphs with many odd cycles are studied.

**Key Words **: Square sum graphs,Pl_{m n},TBL(n,α,k,β).

**REFERENCES**

[1] B. D. Acharya, Personal Communication, September, (2011).

[2] Ajitha V, Studies in Graph Theory-Labeling of Graphs, Ph. D. Thesis, Kannur Univeristy, Kannur, (2007).

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[5] J. A. Gallian, A dynamic survey of graph labrling, The Electronic Journal of Combinatorics (DS6), (2005).

[6] Germina K. A. and Reena Sebastian, On square sum Graphs, communicated.

[7] F. Harary, Graph Theory, Addison-Wesley Pub. Comp., Reading, Massachusetts, (1969).

[8] Ersazig and A. Rosa, Magic valuation of finite graphs, Canad. Math. Bull., 13, pp. 451-461, (1970).

[9] K. Ramanjaneyulu, V. Ch. Venkaiah and Kishore Kothapalli, Antimagic labeling of class of planar graphs, Australian Journal of Combinatorics, 41, pp. 283-290, (2008).

[10] J. Baskar Babujee,planar graphs with maximum edge antimagic property, The Mathematics Education, 37 (4), pp. 194-198, (2003).

**Reena Sebastian**

Department of Mathematics,

S. E. S. College,

Sreekandapuram,

India

e-mail: reeshijo@gmail.com

**K. A. Germina**

School of Mathematical and Physical Sciences, Central University of Kerala,

Kasargode,

India

e-mail: srgerminaka@gmail.com

l^{:}First author is indebted to the University Grants Commission(UGC) for granting her Teacher Fellowship under UGC’s Faculty Development Programme during XI plan.

**Received : November 2013. Accepted : February 2015**