A perfect matching of a graph is a matching (i.e., an independent edge set) in which every vertex of the graph is incident to exactly one edge of the matching.
an independent set or stable set is a set of vertices in a graph, no two of which are adjacent.
A maximum independent set is an independent set of largest possible size for a given graph G. This size is called the independence number of G, and denoted α(G)
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Perfect matching exists for only graph with even number of vertices. No graph with odd number of vertices can contain perfect matching
here u get matching for complete graph
http://mathworld.wolfram.com/PerfectMatching.html
https://en.wikipedia.org/wiki/Independent_set_(graph_theory)