A Note on Pair Sum Graphs

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.v3i2.6290J. Sci. Res. 3 (2), 321-329 (2011)