On square sum graphs


  • K. A. Carmina Central University of Kerala.
  • Reena Sebastian S. E. S. College.




Square sum graphs.


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 ∈ 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.


[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.

How to Cite

K. A. Carmina and R. Sebastian, “On square sum graphs”, Proyecciones (Antofagasta, On line), vol. 32, no. 2, pp. 107-117, 1.