Explanation:
Lathyrus odoratus is a plant that has different color variations in its flowers such as purple, pink, white, etc. In this particular case, the cross between two purple flowered plants gave a pink flowered progeny. This indicates that there is a complementary gene interaction involved in the inheritance of flower color in Lathyrus odoratus.

Complementary Gene Interaction:
Complementary gene interaction is a type of gene interaction where two or more genes interact with each other to produce a particular phenotype. In this type of interaction, one gene is responsible for the production of a particular enzyme or protein, while the other gene is responsible for the activation of that enzyme or protein. Without the activation gene, the enzyme or protein produced by the first gene cannot function properly, resulting in a different phenotype.

Incomplete Dominance:
Incomplete dominance is a type of inheritance where the heterozygous condition shows an intermediate phenotype between the two homozygous conditions. In Lathyrus odoratus, if incomplete dominance was involved, the progeny would have shown a phenotype that was a blend of the two parental phenotypes, i.e., purple and white, resulting in a light purple or lavender color.

Co-dominance:
Co-dominance is a type of inheritance where both alleles of a gene are expressed equally in the phenotype of the heterozygous condition. In Lathyrus odoratus, if co-dominance was involved, the progeny would have shown both the purple and white color equally in the phenotype, resulting in a flower with purple and white spots.

Segregation:
Segregation is the separation of alleles during gamete formation. In Lathyrus odoratus, if segregation was involved, the progeny would have shown a 3:1 ratio of purple to white flowers, as predicted by Mendelian genetics.

Therefore, the correct option is D, complementary gene interaction, as it explains the phenomenon of pink flowered progeny resulting from the cross between two purple flowered plants in Lathyrus odoratus.