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## Proyecciones (Antofagasta)

##
*Print version* ISSN 0716-0917

### Proyecciones (Antofagasta) vol.32 no.2 Antofagasta May 2013

#### http://dx.doi.org/10.4067/S0716-09172013000200002

Proyecciones Journal of Mathematics Vol. 32, N^{o} 2, pp. 107-117, June 2013. Universidad Católica del Norte Antofagasta - Chile

**On square sum graphs**

**Germina K. A. **

*Central University of Kerala, India *

**Reena Sebastian**

** S***. E. S. College, 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 given by f * (uv) = *(f *(u)) ^{2} *+ (f (v))

^{2}

*for every uv*G E(G)

*is injective. In this paper we initiate a study on square sum graphs and prove that trees, unicyclic graphs, mC*>

_{n},m*1,cycle with a chord, the graph obtained by joining two copies of cycle C*= P2

_{n}by a path Pk and the graph defined by path union of k copies of C_{n}, when the path P_{n}*are square sum.*

**Key Words : ***Square sum graphs.*

**REFERENCES**

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

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

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

[4] J.A.Gallian, Graph labeling (Fifteenth edition), Electronic Journal of Combinatorics 19 (2012)

**Germina K. A.**

Department of Mathematics,

School of Mathematical and Physical Sciences,

Central University of Kerala,

Kasaragode,

India

e-mail : srgerminaka@gmail.com

**Reena Sebastian**

Department of Mathematics,

S. E. S College,

Sreekandapuram,

Kerala,

India

e-mail : reeshijo@gmail.com

Received : July 2012. Accepted : March 2013