On r-Dynamic Chromatic Number of the Corronation of Path and Several Graphs

Abstract

This study is a natural extension of k -proper coloring of any simple and connected graph G. By a n rdynamic

coloring of a graph G, we mean a proper k coloring of graph G such that the neighbors of any vertex v

receive at least min{r, d(v)} different colors. The r-dynamic

chromatic number, written as r(G), is the minimum k such

that graph G has an r-dynamic k -coloring. In this paper we will study the r-dynamic chromatic number of the coronation of path and several graph. We denote the corona product of G and H by 𝐺 ⨀ 𝐻. We will obtain the r-dynamic chromatic number of 𝜒𝑟 )and 𝜒𝑟 (𝑃𝑛 ⨀𝑃𝑚 ), 𝜒𝑟 (𝑃𝑛 ⨀𝐶𝑚 (𝑃𝑛 ⨀𝑊𝑚 ) for m, n 3.