On Achromatic Coloring of Corona Graphs

Abstract

Let \(G = (V(G),E(G))\) be a simple graph and an achromatic coloring of \(G\) is a proper vertex coloring of \(G\) in which every pair of colors appears on at least one pair of adjacent vertices. The achromatic number of \(G\) denoted by \(\psi(G)\), is the greatest number of colors in an achromatic coloring of \(G\). In this paper, we find out the achromatic number for Corona graph of Cycle with Path graphs on the same order \(n\), Path with Cycle graphs on the same order \(n\), Path with Complete graphs on the same order \(n\), Path of order \(n\) with Star graph on order \(n+1\), Path with Wheel graphs on the same order \(n\) and Ladder graph with Path graph on the same order \(n\).