Abstract
An r-dynamic coloring of a graph G is a proper coloring c of the vertices such that c(N(v))≥minr,d(v), for each v∈V(G), where N(v) and d(v) denote the neighborhood and the degree of v, respectively. 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 δ-dynamic chromatic number of middle, total, and central of helm graph, where δ=minv∈V(G)d(v).
Highlights
Throughout this paper all graphs are finite and simple
An upper bound for the dynamic chromatic number of a d-regular graph G in terms of (G) and the independence number of G, (G), was introduced in Dehghan and Ahadi (2012)
We find the -dynamic chromatic number for middle, total, and central graph of helm graph
Summary
Throughout this paper all graphs are finite and simple. The r-dynamic chromatic number was first introduced by Montgomery (2001). An r-dynamic coloring of a graph G is a map c from V(G) to a set of colors such that (i) if uv ∈ E(G), c(u) ≠ c(v), and (ii) for each vertex N. Mohanapriya is working as an assistant professor in the Department of Mathematics, RVS Technical Campus—Coimbatore, Tamil Nadu, India. J. Vernold Vivin is working as an assistant professor in the Department of Mathematics, University College of Engineering Nagercoil, (Anna University, Constituent College), Konam, Nagercoil.
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