ON r-DYNAMIC COLORINGS OF THE FRIENDSHIP GRAPH FAMILIES
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Coloring of graphs is an important area in graph theory with numerous applications including the most famous problems related to graphs. An r-dynamic coloring of a graph G is a proper coloring c of the vertices such that |c(N(v))| ≥ min {r, d(v)}, for each vertex v ∈ V (G). The r-dynamic chromatic number of a graph G is the minimum k such that G has an r-dynamic coloring with k colors. In this paper, we obtain the r-dynamic chromatic number of Pn + Fn, Kn + Fn, L(Fn) and central graphs of the friendship graph.
Abstract
Coloring of graphs is an important area in graph theory with numerous applications including the most famous problems related to graphs. An r-dynamic coloring of a graph G is a proper coloring c of the vertices such that |c(N(v))| ≥ min {r, d(v)}, for each vertex v ∈ V (G). The r-dynamic chromatic number of a graph G is the minimum k such that G has an r-dynamic coloring with k colors. In this paper, we obtain the r-dynamic chromatic number of Pn + Fn, Kn + Fn, L(Fn) and central graphs of the friendship graph.
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