On Achromatic coloring of certain classes of transformation graphs G−+–

Abstract

Let G be an n-vertex graph having n ≥ 3. The transformation graph G−+− of this G is the graph with the union of vertex set and edge set in which the adjacency of two vertices a and b is defined as follows: (i) a and b in V (G) are adjacent if and only if they are non-adjacent in G (ii) a and b in E(G) are adjacent if and only if they are adjacent in G (iii) one of a and b is in V (G) while the other is in E(G), and they are not incident in G. In this paper, we obtain the achromatic coloring of transformation graph G−+− of path graph, sunlet graph, friendship graph, ladder graph, tadpole graph, bistar graph and cycle graph.