R-Dynamic Coloring on Snark Families. (May 2020) - Gomathi, C.S.; Mohanapriya, N.; Dafik, D.
Abstract: An r-dynamic coloring of a graph is a proper minimum coloring of the vertices such that | c ( N ( υ ) ) | ≥ min r, d e g G ( υ ) , for each υ ∈ V ( G ) and it is denoted by χ r ( G ) . Snark are bridgeless cubic connected graph in which every vertex has three neighbors. In this paper, we shown the r-dynamic coloring for Celmins-swart snark, Double star snark, Loupekine snark, Szekeres snark, Watkins snark and infinite family of flower snark with its special case as Tietze's graph. This result reinforce that most of the snark are 6-colorable for its maximum degree and also we give the procedures to construct a r-dynamic coloring of each snark.