Coloring the square of the Cartesian product of two cycles
نویسندگان
چکیده
The square G2 of a graph G is defined on the vertex set of G in such a way that distinct vertices with distance at most two in G are joined by an edge. We study the chromatic number of the square of the Cartesian product Cm2Cn of two cycles and show that the value of this parameter is at most 7 except when m = n = 3, in which case the value is 9, and when m = n = 4 or m = 3 and n = 5, in which case the value is 8. Moreover, we conjecture that for every G = Cm2Cn, the chromatic number of G2 equals the size of a maximal independent set in G2.
منابع مشابه
b-coloring in Square of Cartesian Product of Two Cycles
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عنوان ژورنال:
- Discrete Mathematics
دوره 310 شماره
صفحات -
تاریخ انتشار 2010