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T -Coloring on Certain Graphs

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Page 1: T -Coloring on Certain Graphs

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 graph퐺 = (푉,퐸) and a set T of non-negative integers containing 0, a T -coloring of G is an integer function 푓 of the vertices of G such that |푓(푢)− 푓(푣)| ∉ 푇 whenever 푢푣 ∈퐸. The edge-span of a 푇-coloring is the maximum value of |푓(푢) − 푓(푣)| over all edges 푢푣, and the 푇- 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, 푇 = {0, 푠, 2푠, … 푘푠} ∪ 푆, where s and 푘 ≥ 1 and 푆 ⊆ {푠 + 1, 푠 + 2, …푘푠 − 1}.