Discrete Mathematics with Graph Theory (3rd Edition) 305

Discrete Mathematics with Graph Theory (3rd Edition) 305 -...

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Section 11.2 (c) The given matrices are the adjacency matrices of the digraphs 91 and 92 shown. The map 'P defined by is an isomorphism 91 ~ 92. Thus, A2 = P A 1 PT where 0 1 0 0 0 0 0 0 1 0 P= 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 17. (a) [BB] Each of these graphs is strongly connected; each is a cycle. (b) Each of these graphs is strongly connected; each is a cycle. 303 (c) Neither graph is strongly connected. Each has a vertex of outdegree 0 from which travel is clearly not possible. (d) The graph on the left is not strongly connected because it has a vertex of outdegree 0 from which
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Unformatted text preview: travel is not possible. The one on the right is strongly connected, as can be seen by checking all pairs of vertices (in each direction). 18. (a) [BB] There are just two possibilities for the outdegree sequence; 1,1,1 and 2,1, O. The corre-sponding graphs are shown. vv (b) There are just four possibilities for the outdegree sequence: 3,2,0,1; 3,1,1,1; 2,2,2,0 and 2, 2, 1, 1. The correspondence graphs are these....
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