On the Rainbow Neighbourhood Number of Mycielski Type Graphs

Abstract

A rainbow neighbourhood of a graph G is the closed neighbourhood N [v] of a vertex v ∈ V (G) which contains at least one colored vertex of each color in the chromatic coloring C of G. Let G be a graph with a chromatic coloring C defined on it. The number of vertices in G yielding rainbow neighbourhoods is called the rainbow neighbourhood number of the graph G, denoted by r χ (G). In this paper, we discuss the rainbow neighbourhood number of the Mycielski type graphs of graphs.