A different approach for multi-level distance labellings of path structure networks

For a positive integerk, a radiok-labelling of a simple connected graph G= (V,E) is a mapping f from the vertex set V(G) to a set of non-negative integers such that |f(u) - f(v)| >= k+ 1 - d(u,v) for each pair of distinct vertices u and vof G,where d (u, v) is the distance between u and v in G. The span of a radio k-coloring f, denoted by span(f)(G), is defined as max(v is an element of V(G)) f(v) and the radio k-chromatic number of G, denoted by rc(k()G), is min(f) {span(f)(G)}where the minimum is taken over all radio k-labellings of G. In this article, we present results of radiok-chromatic number of path P-n for k is an element of {n-1, n-2 ,n-3} in different approach but simple way.