A Note on Pair Sum Graphs

Authors

  • R. Ponraj Sri Paramakalyani College, Alwarkurichi-627412, India
  • J. X. V. Parthipan St. John?s College, Palayamcottai- 627002, India
  • R. Kala Manonmaniam Sundaranar University, Tirunelveli-627012, India

DOI:

https://doi.org/10.3329/jsr.v3i2.6290

Keywords:

Cycle, Path, Bistar, Complete Graph, Complete bipartite graph, Triangular snake.

Abstract

Let G be a (p,q) graph. An injective map ƒ: V (G) {±1, ±2,...,±p} is called a pair sum labeling if the induced edge function, ƒe: E(G)→Z -{0} defined by ƒe (uv)=ƒ(u)+ƒ(v) is one-one and ƒe(E(G)) is either of the form {±k1, ±k2,…, ±kq/2} or k1, ±k2,…, ±k(q-1)/2} {k (q+1)/2} according as q is even or odd. Here we prove that every graph is a subgraph of a connected pair sum graph. Also we investigate the pair sum labeling of some graphs which are obtained from cycles. Finally we enumerate all pair sum graphs of order ≤ 5.

Keywords: Cycle; Path; Bistar; Complete graph; Complete bipartite graph; Triangular snake.

© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.

doi:10.3329/jsr.v3i2.6290                 J. Sci. Res. 3 (2), 321-329 (2011)

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Author Biographies

R. Ponraj, Sri Paramakalyani College, Alwarkurichi-627412, India

Department of Mathematics

Sri Paramakalyani College, Alwarkurichi-627412, India

 

J. X. V. Parthipan, St. John?s College, Palayamcottai- 627002, India

 

Department of Mathematics

St. John’s College, Palayamcottai- 627002, India

 

R. Kala, Manonmaniam Sundaranar University, Tirunelveli-627012, India

Department of Mathematics

Manonmaniam Sundaranar University, Tirunelveli-627012, India

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Published

2011-04-28

How to Cite

Ponraj, R., Parthipan, J. X. V., & Kala, R. (2011). A Note on Pair Sum Graphs. Journal of Scientific Research, 3(2), 321–329. https://doi.org/10.3329/jsr.v3i2.6290

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Section

Section A: Physical and Mathematical Sciences