Figure Prob 2.1a shows a digraph. Motion can go along an arc only in the direction indicated. Starting at node 1, to what nodes is motion allowed to go (using directed paths)? Include Node 1 itself. Do the same for starting at nodes 2,3,4,5,6,7.
A digraph is strongly connected if there is a directed path from any node to any other node. Is the digraph in figure Prob 2.1a strongly connected? Is the underlying ugraph connected?
The adjacent figure Prob 2.2a shows a ugraph with 16 nodes. The ugraph has several components.
(a) using the figure trace out the components. Assign different colors for the edges of the different compontnts, or draw an equivalent ugraph so that the edges do not overlap, that is, where the components are physically separated from one another.
(b) list all the edges of ugraph in the figure and using the method in the additional material for section 2.2 calculate the nodes in each component.
(c) If the components are separated then for each component delete edges to create a spanning forest.