Multi-Fractional Domination

Abstract

As an extension of the fractional domination and fractional domatic graphical parameters, multi-fractional domination parameters are introduced. We demonstrate the Linear Programming formulations, and to these formulations we apply the Partition Class Theorem, which is a generalization of the Automorphism Class Theorem. We investigate some properties of the multi-fractional domination numbers and their relationships to the fractional domination and fractional domatic numbers.