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For the following graph G, let X denote the set of vertices in G that have even distances from vertex z and let Y = V(G)\X. W UL (a) Determine X and Y. (b) Are both X and Y independent sets? (c) If X is not independent, is there an odd cycle C in G which contains two ver- tices in X?

For the following graph G, let X denote the set of vertices in G that have even distances from vertex z and let Y = V(G)\X. W UL (a) Determine X and Y. (b) Are both X and Y independent sets? (c) If X is not independent, is there an odd cycle C in G which contains two ver- tices in X?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For the following graph G, let X denote the set of vertices in G that have even distances from vertex z and let Y = V(G)\X. WA U (a) Determine X and Y. (b) Are both X and Y independent sets? (c) If X is not independent, is there an odd cycle C in G which contains two ver-. tices in X?
Transcribed Image Text:For the following graph G, let X denote the set of vertices in G that have even distances from vertex z and let Y = V(G)\X. WA U (a) Determine X and Y. (b) Are both X and Y independent sets? (c) If X is not independent, is there an odd cycle C in G which contains two ver-. tices in X?
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