R – Number Of Some Families Of Graphs

Document Type : Primary Research paper

Authors

1 Research Department of Mathematics, VHN Senthikumara Nadar College (A) Virudhunagar – 626001, India.

2 Research Department of Mathematics , VHN Senthikumara Nadar College (A) Virudhunagar – 626001, India.

Abstract

Let G(V(G),E(G)) be a simple connected graph. An injective function f : V (G)
→ {1, 2, 3, ...} is said to be an R-labeling if it satisfies the following conditions: |f (u) − f
(v)| ≥ 2, if d(u, v) = 1 ; |f (u) − f (v)| ≥ 1, if d(u, v) = 2, for any two distinct vertices u, v ∈ V
(G). The span of an R−labeling, f , is the largest integer in the range of f and is
denoted by fR. The R− number, R(G) or R of G is the minimum span taken over all R−
labelings of G. In this paper, we determine the R – number of some families of
graphs.

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