Abstract

A matching of a graph G is called a maximal matching if it is not properly contained in any matching of G. The average size of a maximal matching ofG, avm(G), is the average value taken over the sizes of all maximal matchings of G. Which graphs G have the maximum or minimum value of avm(G) when G is restricted to a particular family? We answer this question, with a full characterization of the extremal graphs, in the families of trees, (connected) unicyclic graphs, trees with a fixed diameter d≤5, and 2-regular graphs.

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