Question

4. Based on the following graph G, compute the matrices M, M², M3, M4 and (M + M2 + M3 + M4), and then use them to answer the following questions about graph G. A B D Graph, G a. How many walks of length 4 are there from node B to node E? b. How many walks are there from node D to node E of length less than or equal to 4? C. Give a complete list of those walks as stated in part (b). [15 marks]

Answer 1

solution: The given graph G is a are dinected). diagraph (all edges B E C 23 matrix M adjacency Firest wel need to find the and Me single edge reachable (a path having single edge) Put I, where a single edge path exist, otherwise put ő B E A - A 0 1 ! o 1 1 0 M= - C 0 o - 0 1 0 0 1 O w?? 2. Two edge reachable ( a path having too edge) But o. if no such path exist exactly one such par exist two such path exist and if 1 2. if soon... A B C E 2 0 1 A Now B 0 o 2 2 2 1 0 0 0 - DI E 0 0 1 0 1 0

MB: 3. edge reachable E А Al 2 B 1 C 0 2 0 - 2. 1 0 2 M c 0 O 2 2 2 2 o 2 0 EO 0 2 2 Similarly for aft: 4-edge rechable B C E A 4 3 1 2 0 A dd - یا 2 M4= C 0 O - ooo la 2 д 2 0 £10 0 0 2 A 5 Now wh tu? tug tugt B F 2 4 3 3 5 6 4 5 8 ។ 2 4 Y 3 3 4 2 13 24 1 6 2 From B to E, there is one walk having lengthy. having length 24 arce 2 walks (b from D to E, there length 1 : DE length length lengthy: Nit, iD-E-E 3: NY