Abstract: Let G=(V,E) be a graph. A real-valued function f∶V→[0,1] is said to be a fractional dominating function (FDF) if f(N[u])≥1 holds for every vertex u∈V(G). The fractional domination number γ_f(G) of G is defined as γ_f(G)=min{f(V)|f is a FDF of graph G}. In this paper, the exact values of γ_f(K_m×P_n),γ⁰_f(K_m×P_n) for all integers m≥3, n≥2, andγ_f(K_m∨P_n) for all integers m≥5, n≥3 are given.

Key words: graph, product graph, join graph, fractional dominating function, fractional domination number