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Recall that P7 is the graph with vertices V = {1,2, 3, 4, 5, 6,7} and edges E = {{1,2}, {2, 3}, {3,4}, {4, 5}, {5, 6}, {6,7}}. Let An be the number of walks of length 2n on P7 starting at vertex 1. (a) Show that an satisfies the recurrence relation an = E 4аn-1 — 2ан-2. Hint: Show by induction that the number an, bn, Cn, and dn of walks starting at vertex 1, 3, 5, and 7, respectively, all satisfy the same recurrence relation.

Recall that P7 is the graph with vertices V = {1,2, 3, 4, 5, 6,7} and edges E = {{1,2}, {2, 3}, {3,4}, {4, 5}, {5, 6}, {6,7}}. Let An be the number of walks of length 2n on P7 starting at vertex 1. (a) Show that an satisfies the recurrence relation an = E 4аn-1 — 2ан-2. Hint: Show by induction that the number an, bn, Cn, and dn of walks starting at vertex 1, 3, 5, and 7, respectively, all satisfy the same recurrence relation.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter12: Angle Relationships And Transformations
Section12.5: Reflections And Symmetry
Problem 20E
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Recall that P7 is the graph with vertices V = {1,2, 3, 4, 5, 6, 7} and edges E = {{1,2}, {2, 3}, {3,4}, {4, 5}, {5, 6}, {6,7}}. Let an be the number of walks of length 2n on P7 starting at vertex 1. (a) Show that an satisfies the recurrence relation 4аn-1 — - 2an-2. An = Hint: Show by induction that the number a,, bn, Cn, and dn of walks starting at vertex 1, 3, 5, and 7, respectively, all satisfy the same recurrence relation.
Transcribed Image Text:Recall that P7 is the graph with vertices V = {1,2, 3, 4, 5, 6, 7} and edges E = {{1,2}, {2, 3}, {3,4}, {4, 5}, {5, 6}, {6,7}}. Let an be the number of walks of length 2n on P7 starting at vertex 1. (a) Show that an satisfies the recurrence relation 4аn-1 — - 2an-2. An = Hint: Show by induction that the number a,, bn, Cn, and dn of walks starting at vertex 1, 3, 5, and 7, respectively, all satisfy the same recurrence relation.
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