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Proyecciones (Antofagasta)

versión impresa 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 Plm,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,Plm n,TBL(n,α,k,β).


REFERENCES

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

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

[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).         [ Links ]

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

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

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