L(2,1) Labeling For Regular Graphs

Abstract

A k − L(2,1) labeling f for a given graph G = (V, E) , is a function f :V →{0,1,2, ...,k} such that for every pair of vertices x, y in V , f ( x) − f ( y) ≥ 2 if d ( x, y) = 1 , and f ( x) − f ( y) ≥ 1 if d ( x, y) = 2 where d ( x, y) denotes the distance between vertices x and y. The L(2,1) labeling problem is finding the minimum k such that G has a k − L(2,1) labeling. This paper established the bounds of L(2,1) labeling, for some regular graphs such as star-like, pancake, burnt pancake, and folded hypercube graph.