On r-dynamic k-coloring of ladder graph families

Abstract

The concept of r-dynamic k-coloring of a graph G refers to a proper vertex k-coloring where the number of colors assigned to the vertices in the neighborhood of each vertex v is greater than or equal to the min {r, Delta(G)}. This study focuses on the r-dynamic coloring of various types of ladder graphs, which are derived from the Cartesian product of P2 and Pn, including the Diagonal Ladder Graph, Open Diagonal Ladder Graph, Triangular Ladder Graph, Open Triangular Ladder Graph and Slanting Ladder Graph.