Given a graphG=(V,E) and a set T of non-negative integers containing 0, a T -coloring of G is an integer function f of the vertices of G such that |f(u)-f(v)|∉T whenever uv∈E. The edge-span of a T-coloring is the maximum value of |f(u)-f(v)| over all edges uv, and the T- edge-span of a graph G is the minimum value of the edge-span among all possible T -colorings of G. This paper discusses the T -edge span of the folded hypercube network of dimension n for the k-multiple-of-s set, T={0,s,2s,…ks}∪S, where s and k≥1 and S⊆{s+1,s+2,…ks-1}.

1. International Journal of Computing Algorithm, Vol 3(2), June 2014
ISSN(Print):2278-2397
Website: www.ijcoa.com
T -Coloring on Certain Graphs
Antony Xavier1
, R.C. Thivyarathi2
1
Department of Mathematics, Loyola College, Chennai
2
Department of Science and Humanities, R.M.D Engineering College, Chennai
Abstract
Given a graph = ( , ) and a set T of non-negative integers containing 0, a T -coloring of
G is an integer function of the vertices of G such that | ( ) − ( )| ∉ whenever ∈
. The edge-span of a -coloring is the maximum value of | ( ) − ( )| over all edges ,
and the - edge-span of a graph G is the minimum value of the edge-span among all possible
T -colorings of G. This paper discusses the T -edge span of the folded hypercube network of
dimension n for the k-multiple-of-s set, = {0, , 2 ,… } ∪ , where s and ≥ 1 and
⊆ { + 1, + 2, … − 1}.