The Lower Bound of the r-Dynamic Chromatic Number of Corona Product by Wheel Graphs
Abstract
The dynamic coloring of a graph G is proper coloring such that every vertex of G with degree has at least two
neighbors that are colored differently. A generalization of the dynamic coloring was also introduced by Montgomery in
[12], the generalized concept is called r-dynamic k-coloring. 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,
denoted r(G) is the smallest k such that c is an r-dynamic k coloring of G. We will find the lower bound of the rdynamic
chromatic
number
of
graphs
corona
wheel
graph
and
some
new
results
the
exact
value
of
r-dynamic
chromatic
number
of
corona graphs. In this paper, we study the lower bound of 𝜒𝑟
(𝐻⨀𝑊𝑚
), 𝜒𝑟(𝑊𝑛⨀𝐻) and we also prove the
exact value of r-dynamic chromatic number of some graphs.
Collections
- LSP-Conference Proceeding [1877]