The complement of a graph G is a new graph formed by removing all the edges of G and replacing them by all possible edges that are not in G. Formally, consider a graph G = (V, E). Then, the complement of the graph G is the graph G = (V, E), where 2. E = {{x, y}|x y, {x,y} ¢ E} Prove that for any graph G, G or G (or both) must be connected.
The complement of a graph G is a new graph formed by removing all the edges of G and replacing them by all possible edges that are not in G. Formally, consider a graph G = (V, E). Then, the complement of the graph G is the graph G = (V, E), where 2. E = {{x, y}|x y, {x,y} ¢ E} Prove that for any graph G, G or G (or both) must be connected.
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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![2. The complement of a graph \( G \) is a new graph formed by removing all the edges of \( G \) and replacing them by all possible edges that are not in \( G \). Formally, consider a graph \( G = (V, E) \). Then, the complement of the graph \( G \) is the graph \( \overline{G} = (V, \overline{E}) \), where
\[
\overline{E} = \{\{x, y\} \mid x \neq y, \{x, y\} \notin E \}
\]
Prove that for any graph \( G \), \( G \) or \( \overline{G} \) (or both) must be connected.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb987d8c1-664b-448b-b573-1ab7f66094f6%2F72af3b00-05d9-478a-bc50-bc333276363c%2F00ytkg8_processed.png&w=3840&q=75)
Transcribed Image Text:2. The complement of a graph \( G \) is a new graph formed by removing all the edges of \( G \) and replacing them by all possible edges that are not in \( G \). Formally, consider a graph \( G = (V, E) \). Then, the complement of the graph \( G \) is the graph \( \overline{G} = (V, \overline{E}) \), where
\[
\overline{E} = \{\{x, y\} \mid x \neq y, \{x, y\} \notin E \}
\]
Prove that for any graph \( G \), \( G \) or \( \overline{G} \) (or both) must be connected.
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