00:01
Hello! so for part a in a graph g, an edge is called a bridge if removing it would increase the number of connected components in g.
00:09
So if g is a connected graph of order n, which means that it has n vertices, and every edge is a bridge, this implies that removing any edge would disconnect the graph, and the only type of graph that satisfies this condition is going to be a tree.
00:28
So a tree is a connected graph with no cycles, and the number of edges in a tree is always one less than the number of vertices.
00:38
So therefore the size of g is just the number of edges is going to be n -1.
00:47
And then for b, in the case of a disconnected graph of order n having k components, where every edge is a bridge, each component must be a tree since the removal of any edge would otherwise not disconnect the graph further.
01:05
So each tree -like component will have a number of edges one less than its number of vertices.
01:11
So if the graph has k components, then the total number of edges will be the sum of the number of edges in each component...