# On square sum graphs

## DOI:

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

Square sum graphs.## 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))*+ (f (v))

^{2}^{2}

*for every uv*∈ 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*= P

_{n}by a path P_{k}and the graph defined by path union of k copies of C_{n}, when the path P_{n}_{2}

*are square sum.*

## 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), #DS6.

[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), #DS6.

## How to Cite

[1]

K. A. Carmina and R. Sebastian, “On square sum graphs”,

*Proyecciones (Antofagasta, On line)*, vol. 32, no. 2, pp. 107-117, 1.## Issue

## Section

Artículos