A domination vertex coloring of G is a proper vertex coloring in which each vertex of G dominates at least one color class and each color class is dominated by at least one vertex. The minimum number of colors among all domination coloring is called the domination chromatic number. An equitable coloring of a graph G is a proper coloring of the vertices such that color classes differ in size by at most one. In this paper, we discuss the notion of domination equitable coloring and determine the domination equitable chromatic number of some ladder graphs, namely, closed ladder, open ladder, slanting ladder, and triangular ladder.

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Domination Equitable Coloring for Family of Ladder Graphs

  • Rebekal Haribabu,
  • Sharmila Mary Arul

摘要

A domination vertex coloring of G is a proper vertex coloring in which each vertex of G dominates at least one color class and each color class is dominated by at least one vertex. The minimum number of colors among all domination coloring is called the domination chromatic number. An equitable coloring of a graph G is a proper coloring of the vertices such that color classes differ in size by at most one. In this paper, we discuss the notion of domination equitable coloring and determine the domination equitable chromatic number of some ladder graphs, namely, closed ladder, open ladder, slanting ladder, and triangular ladder.