On r- Dynamic coloring of the gear graph families





r− dynamic coloring, Gear graph, Middle graph, Central graph and line graph


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 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 the middle, central and line graphs of the gear graph.

Author Biographies

T. Deepa, Kongunadu Arts and Science College (Autonomous).

Department of Mathematics.

D. Dafik, University of Jember.

CGANT Research Group, Dept. of Mathematics Education.


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How to Cite

T. Deepa, M. Venkatachalam, and D. Dafik, “On r- Dynamic coloring of the gear graph families”, Proyecciones (Antofagasta, On line), vol. 40, no. 1, pp. 01-15, Jan. 2021.




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