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On the dynamic coloring of cartesian product graphs

Akbari, S ; Sharif University of Technology

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  1. Type of Document: Article
  2. Abstract:
  3. Let G and H be two graphs. A proper vertex coloring of G is called a dynamic coloring, if for every vertex v with degree at least 2, the neighbors of v receive at least two different colors. The smallest integer k such that G has a dynamic coloring with k colors denoted by χ2(G). We denote the cartesian product of G and H by G□H. In this paper, we prove that if G and H are two graphs and δ(G) ≥ 2, then χ2(G□H) ≤ max(χ2(G),x(H)). We show that for every two natural numbers m and n, m,n ≥ 2, χ2(Pm□Pn) = 4. Also, among other results it is shown that if 3|mn, then χ2(C m□Cn) = 3 and otherwise χ2(C m□Cn) = 4
  4. Keywords:
  5. Cartesian product of graphs ; Dynamic coloring
  6. Source: Ars Combinatoria ; Vol. 114 , 2014 , pp. 161-168 ; ISSN: 03817032