2 research outputs found
On conditional coloring of some graphs
For integers r and k > 0(k>r),a conditional (k, r)-coloring of a graph G is a
proper k-coloring of G such that every vertex v of G has at least min{r,d(v)}
differently colored neighbors, where d(v) is the degree of v. In this note, for
different values of r we obtain the conditional chromatic number of a grid
, and the strong product of and
(n,m being positive integers). Also, for integers and the second order conditional chromatic number (also known as dynamic
chromatic number) of the (t,n)-web graph is obtained.Comment: 9 pages: accepted for the 76th annual conference of the Indian
Mathematical Society,27-30 December 2010,Surat,Indi
Conditional and Unique Coloring of Graphs
For integers , a conditional -coloring of a graph is a
proper -coloring of the vertices of such that every vertex of degree
in is adjacent to at least differently colored
vertices. Given , the smallest integer for which has a conditional
-coloring is called the th order conditional chromatic number
of . We give results (exact values or bounds for ,
depending on ) related to the conditional coloring of some graphs. We
introduce \emph{unique conditional colorability} and give some related results.
(Keywords. cartesian product of graphs; conditional chromatic number; gear
graph; join of graphs.)Comment: Under review in International Journal of Computer Mathematic