Explanation Algorithm used: Depth First Search Algorithm. Step 1 (label the starting vertex) Select a vertex U , assign U the label L , and let U have no predecessor. Set L = { U } and T = ϕ . Set k = 2 and X = U . Step 2 (label other vertices) Repeat Step 2.1 (label a vertex adjacent to X ) While there is a vertex Y not in L that is adjacent to X . ( Place the edge { X , Y } in T Assign X to be the predecessor of Y . Assign Y the label k . Include Y in C . Replace k with k + 1 . Now let X denote the vertex Y . Endwhile Step 2.2 (back up) Replace X with the predecessor of X . Until X = null or every vertex of G is in L Step 3 (is there a spanning tree?) If every vertex of G is in L . The edges in T and their incident vertices form a spanning tree of Q Otherwise There is no spanning tree for G because Q is not connected. Endif Theorem 5.7. If the depth-first search algorithm is applied to the graph G . The edge in T and the vertices in L forms a tree. Furthermore, if G is connected, this tree is a spanning tree. Back edges . In a connected graph which follows the theorem 5.7, if T represents the edges in T which formulates a spanning tree and v represents the set of edges v − T are the back edges

5th Edition

ISBN: 9780134689562

Author: Dossey, John A.

Publisher: Pearson,

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Chapter 5.3, Problem 16E

To determine

To list: The back edges in the given graph with the help of depth-first search algorithm.

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Chapter 5.3, Problem 15E

Chapter 5.3, Problem 17E

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Ch. 5.1 - Seven farming communities in Iowa want to develop...Ch. 5.1 - As few trails as possible are to be built between...Ch. 5.1 - A farmer needs to irrigate the fields in which his...Ch. 5.1 - Draw a graph that is not a tree for which the...Ch. 5.1 - Prob. 15E Ch. 5.1 - What is the smallest number of edges in a...Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - There are two saturated hydrocarbons of the type...Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - In order to count the number of distinct trees...Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - In order to count the number of distinct trees...Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - 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