Walks and Paths
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Let \(\{a,b,c,d\}\) be four vertices of a directed graph.
Let \(E(G) = \{(a,b),(a,c),(a,d),(b,c),(b,d),(c,b),(c,d)\}\).
What is the length of the longest path?An example of a longest path in this graph is \(a~(a,b)~b~(b,c)~c~(c,d)~d\)
Recall that the length of a path is defined as the number of edges the path uses.
Also recall that a path cannot have repeated vertices, so we know this path is (one of) the longest because it uses all the vertices.
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If the sum of all the numbers in an adjacency matrix is equal to 6, what does this imply?
The adjacency matrix represents the edges in a digraph.