Floral self-incompatibility affecting yearly yield in a weather-dependent manner and graft incompatibility affecting longevity of mature trees are two important traits for apricot production. However, genetic control of graft compatibility and relationship between these traits are unknown. Here, we analyzed its inheritance in an F1 apricot progeny from a cross between self- and graft- incompatible and self- and graft-compatible cultivars. Hybrid individuals were genotyped for establishing self-incompatibility status and grafted on the plum rootstock 'Marianna 2624'. Phenotyping of graft incompatibility was done at two time points, one month and one year after grafting. Anatomical (necrotic layer, bark and wood discontinuity for two consecutive years) and cytomorphological (cell proliferation, cell arrangement and cell shape one month after grafting) characteristics related to graft compatibility displayed continuous variation within the progeny, suggesting a polygenic inheritance. Using the Pearson correlation test, strong and significant correlations were detected between anatomical and cytomorphological traits that may reduce the number of characters for screening genotypes or progenies for graft compatibility in segregating crosses. Furthermore, no correlation existed between self- and graft incompatibility traits suggesting that they are independent inheritance traits. Hence, screening an extended hybrid population is required for pyramiding these traits in breeding programs.