Since the method for creating a spanning tree with n vertices and m edges is to delete (m - n + 1) edges, a graph may contain more than one spanning tree.
There are n-1 edges in the spanning tree, where n is the number of nodes (vertices). We can create a spanning tree from a full graph by eliminating no more than maximum e - n + 1 edges. There can be a maximum of nn-2 spanning trees in a full graph. In order to create a spanning tree from a linked network with vertices and edges, m - (n - 1) = m - n + 1 edges must be deleted. If the graph has n edges and no cycles, then every spanning tree has n - 1 edges. The MST adheres to the cut property; if an edge (e) from a cut of the graph has a weight that is lower than any other edge from that cut, the edge e is present in all MSTs for that cut.
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