In an undirected graph, the degree d(u) of a vertex u is the number of neighbors u has, or equivalently, the number of edges incident upon it. In a directed graph, we distinguish between the indegree din(u), which is the number of edges into u, and the outdegree dout (u), the number of edges leaving u.
(a) Show that in an undirected graph, ∑uϵVd(u) = 2| E |.
(b) Use part (a) to show that in an undirected graph, there must be an even number of vertices whose degree is odd.
(c) Does a similar statement hold for the number of vertices with odd indegree in a directed graph?
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.