The fractional matching preclusion number of complete n-balanced k-partite graphs

The fractional matching preclusion number of a graph G, denoted by fmp(G), is the minimum number of edges whose deletion results in a graph with no fractional perfect matchings. Let $$G_{k,n}$$ G k , n be the complete n-balanced k-partite graph, whose vertex set can be partitioned into k parts, each has n vertices and whose edge set contains all edges between two distinct parts. In this paper, we prove that if $$k=3$$ k = 3 or 5 and $$n=1$$ n = 1 , then $$fmp(G_{k,n})=\delta (G_{k,n})-1$$ f m p ( G k , n ) = δ ( G k , n ) - 1 ; otherwise $$fmp(G_{k,n})=\delta (G_{k,n})$$ f m p ( G k , n ) = δ ( G k , n ) .