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On \(r\)-dynamic coloring of double star graph families. (English) Zbl 1458.05068

Summary: An \(r\)-dynamic proper \(k\)-coloring of a graph \(G\) is a proper \(k\)-coloring of \(G\) such that every vertex in \(V(G)\) has neighbors in at least \(\min\{r,d(v)\}\) different color classes. 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 investigate the \(r\)-dynamic chromatic number for the central graph, middle graph, total graph and line graph of double star graph.

MSC:

05C15 Coloring of graphs and hypergraphs
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References:

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