I have a graph G with 13 vertices and I need to find a maximum matching and then prove it. If I find a matching containing 6 edges or 12 out of the 13 vertices can I say it's maximum because I cannot add any edges because there is only one vertex remaining as my proof?
Edit. I have this graph and I need to determine a maximum matching and then prove it. I found a matching containing 12 out of the 13 vertices.Can I say it's maximum because I cannot add any other edge as my proof.
If you cannot add any edges, then it is maximal. But if you have all but one edges and you can't add the remaining edge, as in your case, then it is maximum as well as maximal (because the only way to make it larger is to add the remaining edge).