Definition. Given a graph G = (VG, EG) that is connected and contains at least two edges, we say that G is extra-connected if removing any two edges from G results in a connected graph. (a) Give an example of a graph that is extra-connected. Briefly explain why your graph qualifies. (b) Give an example of a graph that is connected but not extra-connected. Briefly explain why your graph qualifies. (c) Definition. Given a graph G = (VG, EG) that is connected, we say that G is super-connected if, for every vertex v € VG, removing v and all edges incident with v from G results in a connected graph. Is every super-connected graph also extra-connected? Justify your claim. (d) Conversely, is every extra-connected graph also super-connected? Justify your claim.
Definition. Given a graph G = (VG, EG) that is connected and contains at least two edges, we say that G is extra-connected if removing any two edges from G results in a connected graph. (a) Give an example of a graph that is extra-connected. Briefly explain why your graph qualifies. (b) Give an example of a graph that is connected but not extra-connected. Briefly explain why your graph qualifies. (c) Definition. Given a graph G = (VG, EG) that is connected, we say that G is super-connected if, for every vertex v € VG, removing v and all edges incident with v from G results in a connected graph. Is every super-connected graph also extra-connected? Justify your claim. (d) Conversely, is every extra-connected graph also super-connected? Justify your claim.
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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Transcribed Image Text:Definition. Given a graph G = (VG, EG) that is connected and contains at least two edges, we
say that G is extra-connected if removing any two edges from G results in a connected graph.
(a) Give an example of a graph that is extra-connected. Briefly explain why your graph
qualifies.
(b) Give an example of a graph that is connected but not extra-connected. Briefly explain
why your graph qualifies.
(c) Definition. Given a graph G = (VG, EG) that is connected, we say that G is super-connected if,
for every vertex v € VG, removing v and all edges incident with v from G results in a connected
graph.
Is every super-connected graph also extra-connected? Justify your claim.
(d) Conversely, is every extra-connected graph also super-connected? Justify your claim.
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