Application of Multiobjective Optimization Integrating Numerical and Scientific Computing in Graph Theory Coloring Algorithm

Table 1

P_ast of part of graph T.

Figure T	To meet the conditions	Past
Zn	n is odd and n ≥ 3	4
Zn	n is even and n ≥ 3	5
Xn	n ≡ 0 (mod2), n ≠ 4, 10, n ≥ 3	4
Xn	n ≡ 1 (mod2), n = 4, 10, n ≥ 3	5
Cn	n ≥ 3	n + 1
	n = 2, 3	5
	⊗	6
	n ≥ 5	n + 1
Bn	n = 2^k, k = 2, 3, 4, 5	n + k
Bn	n ≥ 3, and ≠6, 14	n + [log2n]
N	∆(N) ≥ 4 and there is no maximum degree point neighbor	∆(N) + 1
N	∆(N) ≥ 4and there is maximum degree point neighbor	∆(N) + 2