On r-dynamic k-coloring of ladder graph families

Abstract

The concept of [Formula: see text]-dynamic [Formula: see text]-coloring of a graph [Formula: see text] refers to a proper vertex [Formula: see text]-coloring where the number of colors assigned to the vertices in the neighborhood of each vertex [Formula: see text] is greater than or equal to the min [Formula: see text]. This study focuses on the [Formula: see text]-dynamic coloring of various types of ladder graphs, which are derived from the Cartesian product of [Formula: see text] and [Formula: see text], including the Diagonal Ladder Graph, Open Diagonal Ladder Graph, Triangular Ladder Graph, Open Triangular Ladder Graph and Slanting Ladder Graph.