English

Conditional coloring of some parameterized graphs

Discrete Mathematics 2010-12-13 v1

Abstract

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 χr(G)\chi_r(G). For different values of r we obtain χr(G)\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.

Keywords

Cite

@article{arxiv.1012.2251,
  title  = {Conditional coloring of some parameterized graphs},
  author = {P. Venkata Subba Reddy and K. Viswanathan Iyer},
  journal= {arXiv preprint arXiv:1012.2251},
  year   = {2010}
}

Comments

Communicated to Utilitas Mathematica

R2 v1 2026-06-21T16:56:30.185Z