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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

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

Proyecciones Journal of Mathematics Vol. 32, No 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


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, mCn,m > 1,cycle with a chord, the graph obtained by joining two copies of cycle Cn by a path Pk and the graph defined by path union of k copies of Cn, when the path Pn = P2 are square sum.

Key Words : Square sum graphs.


[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,
e-mail :

Reena Sebastian
Department of Mathematics,
S. E. S College,
e-mail :

Received : July 2012. Accepted : March 2013

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