On the fractional matching number of the join and corona of graphs

Abstract

A fractional matching of a graph G = (V,E) is a function f from E to the interval [0, 1] such that ∑ e∈Γ(v) f(e) ≤ 1 for every v ∈ V , where Γ(v) is the set of all edges incident to v. The fractional matching number of G, written α′ ∗(G), is the maximum of ∑ e∈E f(e) over all fractional matchings f . In this paper, we gave the fractional matching number of the join of some graphs, and the corona of some graphs. Mathematics Subject Classification: 05C70 Keyword: integral matching number, fractional matching number, join, corona