δ-Dynamic chromatic number of Helm graph families

An r-dynamic coloring of a graph G is a proper coloring c of the vertices such that , for each , 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 pa...

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Bibliographic Details
Published in:Cogent mathematics 2016-12, Vol.3 (1), p.1178411
Main Authors: Mohanapriya, N., Vernold Vivin, J., Venkatachalam, M.
Format: Article
Language:English
Subjects:
05C15
Apexes
central graph
Coloring
Graph theory
middle graph
r-dynamic coloring
total graph
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Summary:An r-dynamic coloring of a graph G is a proper coloring c of the vertices such that , for each , 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 -dynamic chromatic number of middle, total, and central of helm graph, where .
ISSN:2331-1835
2331-1835
2768-4830
DOI:10.1080/23311835.2016.1178411