Let G be the connected graph with n vertices and e edges. The chromatic number of G, χ(G) is the least color count required to color the vertex set V(G) such that no two adjacent vertices are assigned with the same integer [ 1]. χ(G) is determined using different soft computing strategies [ 2,3]. This research gives χ(G) and the optimal coloring assignments for some of the queen graphs that are obtained using the soft computing strategies.

χ(G) = 5

Optimal color assignments:

(3 4 2 5 1 2 5 1 3 4 1 3 4 2 5 4 2 5 1 3 5 1 3 4 2)

(1 2 3 4 5 3 4 5 1 2 5 1 2 3 4 2 3 4 5 1 4 5 1 2 3)

(2 3 4 5 1 4 5 1 2 3 1 2 3 4 5 3 4 5 1 2 5 1 2 3 4)

(3 1 4 5 2 4 5 2 3 1 2 3 1 4 5 1 4 5 2 3 5 2 3 1 4)

(1 2 3 4 5 4 5 1 2 3 2 3 4 5 1 5 1 2 3 4 3 4 5 1 2)

(3 4 1 5 2 1 5 2 3 4 2 3 4 1 5 4 1 5 2 3 5 2 3 4 1)

χ(G) = 7

Optimal color assignments:

(7 1 2 3 4 5 2 3 4 5 6 7 4 5 6 7 1 2 6 7 1 2 3 4 1 2 3 4 5 6 3 4 5 6 7 1)

(5 1 2 3 4 6 2 3 4 6 7 5 4 6 7 5 1 2 7 5 1 2 3 4 1 2 3 4 6 7 3 4 6 7 5 1)

(1 3 6 4 5 7 5 7 2 1 3 6 3 6 4 5 7 2 7 2 1 3 6 4 6 4 5 7 2 1 2 1 3 6 4 5)

(3 2 5 6 7 4 4 6 7 2 1 5 2 5 1 3 6 7 1 4 2 7 5 3 5 7 3 1 4 6 6 1 4 5 3 2)

χ(G) = 7

Optimal color assignments:

(5 6 1 3 4 7 2 7 2 5 6 1 3 4 3 4 7 2 5 6 1 6 1 3 4 7 2 5 2 5 6 1 3 4 7 4 7 2 5 6 1 3 1 3 4 7 2 5 6)

(1 2 3 4 5 6 7 3 4 5 6 7 1 2 5 6 7 1 2 3 4 7 1 2 3 4 5 6 2 3 4 5 6 7 1 4 5 6 7 1 2 3 6 7 1 2 3 4 5)

χ(G) = 9

Optimal color assignments:

(1 2 3 4 5 6 7 8 3 4 1 6 8 2 5 9 5 8 9 7 4 3 6 2 6 7 2 5 9 8 1 4 2 5 6 1 3 4 9 7 9 3 4 2 6 7 8 5 8 6 7 9 1 5 2 3 7 1 5 8 2 9 4 6)

This article presented some of the solutions obtained for queen graphs using evolutionary methods.