For instance, when a conveyance is made to a man, his assent to it is presumed, for the following reasons; cause there is a strong intendment of law, that it is for a person's benefit to take, and no man can be supposed to be unwilling to do that which is for his advantage. 2.
A simple graph, as opposed to a multigraph, is an undirected graph in which both multiple edges and loops are disallowed. In a simple graph the edges form a set (rather than a multiset) and each edge is an unordered pair of distinct vertices.
Show that the following are equivalent definitions for a tree: 1  A graph with a minimal number of edges which is connected. 2  A graph with maximal number of edges without a cycle. 3  A graph with no cycle in which adding any edge creates a cycle.  A graph with n nodes and n-1 edges that is connected.