Abstract
Objectives: Consider a graph is the connected, undirected graph. This study creates a new parameter named the Fractional Star Domination Number (FRSDN), which is denoted by to calculate the minimum weight with the star of all vertices of and the function values of all edges. Methods: This study evaluates the of some standard graphs and bounds by generalizing the value that is provided by the function value of an edges. Findings: This study evaluated on some standard graphs, such as paths, cycles, and the rooted product of paths and cycles. Finally, we obtain some bounds on for some general graphs, as well as the exactness value yielded by them. For any graph without isolated vertices, we have . Novelty: The new parameter FRSDN of is created by combining the fractional dominating function and the star dominating set. Keywords: Domination Number, Star Domination Number, Fractional Dominating Function, Fractional Domination Number, Fractional Star Domination Number
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