Suppose that G = (V, E) is a directed graph. A vertex w E V is called reachable from a vertex v € V if there is a directed path from v to w. The vertices v and w are mutually reachable if there is both a directed path from v to w and a directed path from w to v in G. Show that if G = (V, E) is a directed graph and that u, v and w are vertices in V for which u and v are mutually reachable and v and w are mutually reachable, then u and w are mutually reachable.

Suppose that G = (V, E) is a directed graph. A vertex w E V is called reachable from a vertex v € V if there is a directed path from v to w. The vertices v and w are mutually reachable if there is both a directed path from v to w and a directed path from w to v in G. Show that if G = (V, E) is a directed graph and that u, v and w are vertices in V for which u and v are mutually reachable and v and w are mutually reachable, then u and w are mutually reachable.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.5: The Format Proof Of A Theorem

Problem 12E: Based upon the hypothesis of a theorem, do the drawings of different students have to be identical...

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