Radio 1 - Chromatic Number of Uniform ???? - Cyclic Split Graph and ????-Wheel Star Graph

Abstract

For any integer ????, lies between zero and diameter plus one, a radio ???? −chromatic labelling of a simple connected graph ???? = (????, ????) is a mapping from ????(????) to N such that ????(????, ????) + |????(????) − ????(????)| ≥ 1 + ???? , ∀ ????, ???? ∈ ????(????), where ????(????, ????) is the distance between ???? and ????. The maximum number assigned to a vertex under the mapping ℎ is denoted by ????????????(????), is called the radio ???? - chromatic number of G under the mapping ????. The radio ????- chromatic number of G, denoted by ????????????(????) is the minimum value taken over all such radio ???? - chromatic numbers of ????. In this paper, we have obtained the radio 1-chromatic number of Uniform r - cyclic split graph and ????-wheel star graph.