On r-dynamic vertex coloring of line, middle, total of lobster graph

Abstract

Abstract Let G be a simple, connected and undirected graph that has a set of vertex and edge. The degree of v ∈ V(G) is denoted by d(v). The maximum and minimum degree of G respectively are Δ(G) and δ(G). The r-dynamic color of the graph G is calculated as a map c from V to a color set such that if u, v ∈ V(G) is adjacent, then c(u) ≠ c(v), and for each v ∈ V(G), |c(N(v))| ≥ min{r, d(v)}. The number of r-dynamic coloring of G denoted by χr (G) is minimum color k in G. In this paper, we have obtained the r-dynamic vertex coloring of line, middle, total of lobster graph ℒn (2, 1).