Radio k-colorings of paths

Abstract

For a connected graph G of diameter d and an integer k with 1 ≤ k ≤ d, a radio k-coloring of G is an assignment c of colors (positive integers) to the vertices of G such that d(u, v) + |c(u) − c(v)| ≥ 1 + k * Research supported in part by the Western Michigan University Arts and Sciences Teaching and Research Award Program.

Radio Labelings and Antipodal Labelings of Trees with Order Up to Eight

“…Chartrand et al 1 studied the radio k-labeling number for paths and they gave their lower and upper bounds. Later, Kchikech et al 2 improved these bounds, and they studied the radio k-labelings for the Cartesian product of graphs.…”

Improved upper bounds for nearly antipodal chromatic number of paths

“…Radio k-coloring and radio labeling of graphs were studied in [1,2]. Radio antipodal coloring of paths were studied in [3,4,6].…”

Multi-level and antipodal labelings for certain classes of circulant graphs

“…The study of radio k-labelings was motivated by Chartrand et al [3]. Quite few results concerning radio k-labelings are known.…”

“…Quite few results concerning radio k-labelings are known. Chartrand et al [3] was the first, who studied the radio k-labeling number for paths, where lower and upper bounds were given. These bounds have been improved by Kchikech et al [7].…”

“…The minimum span of an antipodal labeling is called the antipodal number, denoted by an(G). In [1,3], Chartrand et al studied the radio antipodal labeling for cycle and path. In [2], Chartrand et al gave general bounds for the antipodal number of a graph.…”