The radio k-chromatic number for corona of graphs
P. K. Niranjan, Srinivasa Rao Kola · Asian-European Journal of Mathematics · 2022
For a connected simple graph [Formula: see text] and a positive integer [Formula: see text], a radio [Formula: see text]-coloring is an assignment [Formula: see text] of positive integers (colors) to the vertices of [Formula: see text] such that for every pair of distinct vertices [Formula: see text] and [Formula: see text] in [Formula: see text], [Formula: see text]. The span [Formula: see text] of [Formula: see text] is [Formula: see text]. The minimum of [Formula: see text] is a radio [Formula: see text]-coloring of [Formula: see text] is called the radio [Formula: see text]-chromatic number of [Formula: see text] and is denoted by [Formula: see text]. If [Formula: see text] is the diameter of [Formula: see text], then a radio [Formula: see text]-coloring is referred as a radio coloring and the radio [Formula: see text]-chromatic number as the radio number, [Formula: see text], of [Formula: see text]. In this paper, we obtain an upper bound for the radio k-chromatic number of the corona of two graphs [Formula: see text] and [Formula: see text] for [Formula: see text], and we obtain a necessary condition for this upper bound to be exact. Also, we see that for path [Formula: see text], [Formula: see text] even and complete graph [Formula: see text] the upper bound is sharp for [Formula: see text] and [Formula: see text], where [Formula: see text] is an arbitrary graph. Further, we give a lower bound and an improved upper bound for [Formula: see text], [Formula: see text] odd and [Formula: see text], [Formula: see text] is hypercube.