Conditional coloring of some parameterized graphs

Details Conditional coloring of some parameterized graphs Conditional coloring of some parameterized graphs

2010-12-10

arxiv.org/abs/1012.2251v1

Computer Science

Discrete Mathematics

Communicated to Utilitas Mathematica

Scientific paper

For integers k>0 and r>0, a conditional (k,r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex v of degree d(v) in G is adjacent to vertices with at least min{r,d(v)} different colors. The smallest integer k for which a graph G has a conditional (k,r)-coloring is called the rth order conditional chromatic number, denoted by $\chi_r(G)$. For different values of r we obtain $\chi_r(G)$ of certain parameterized graphs viz., Windmill graph, line graph of Windmill graph, middle graph of Friendship graph, middle graph of a cycle, line graph of Friendship graph, middle graph of complete k-partite graph and middle graph of a bipartite graph.

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