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Dominating coloring number of claw-free graphs

Abdolghafurian, A ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1016/j.endm.2013.11.018
  3. Abstract:
  4. Let G be a graph. It is well-known that G contains a proper vertex-coloring with χ(G) colors with the property that at least one color class of the coloring is a dominating set in G. Among all such proper vertex-coloring of the vertices of G, a coloring with the maximum number of color classes that are dominating sets in G is called a dominating-χ-coloring of G. The number of color classes that are dominating sets in a dominating-χ-coloring of G is defined to be the dominating-χ-color number of G and is denoted by dχ(G). In this paper, we prove that if G is a claw-free graph with minimum degree at least two, then dχ(G)≥2
  5. Keywords:
  6. Chromatic number ; Claw-free graph ; Dominating set ; Dominating-χ-color number ; Maximal independent set
  7. Source: Electronic Notes in Discrete Mathematics ; Vol. 45, issue , January , 2014 , pp. 91-97 ; ISSN: 15710653
  8. URL: http://www.sciencedirect.com/science/article/pii/S1571065313002989