On the Dynamic Coloring of Cartesian Product Graphs.
Saieed Akbari, Maryam Ghanbari, Sogol Jahanbekam · San José State University ScholarWorks (San Jose State University) · 2014
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 X2(G).We denote the cartesian product of G and H by GDH.In this paper, we prove that if G and H are two graphs and 8(G) 2: 2, then X2(GDH) max(X2(G), X(H)).We show that for every two natural numbers m and n, m, n 2: 2, X2(PmDPn) = 4. Also, among other results it is shown that if 3lmn, then X2(CmDCn) = 3 and otherwise X2 (Cm DCn) = 4.