. We can consider graphs G=(V,E) with a countably infinite number of vertices. Namely, put V = N so there is one vertex for each natural number. Consider the set of graphs G=(V, E) with V = N such that each connected component contains finitely many vertices. For instance, G = (N, 0) is in our set since all connected components have a single vertex, while G= (N, E) with E= {(n,n+1) | n E N} is not since all vertices are in a single infinite connected component.
. We can consider graphs G=(V,E) with a countably infinite number of vertices. Namely, put V = N so there is one vertex for each natural number. Consider the set of graphs G=(V, E) with V = N such that each connected component contains finitely many vertices. For instance, G = (N, 0) is in our set since all connected components have a single vertex, while G= (N, E) with E= {(n,n+1) | n E N} is not since all vertices are in a single infinite connected component.
Advanced Engineering Mathematics
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Transcribed Image Text:d. We can consider graphs G=(V, E) with a countably infinite number of vertices. Namely, put V = N
so there is one vertex for each natural number. Consider the set of graphs G=(V,E) with V = N such
that each connected component contains finitely many vertices.
For instance, G = (N, 0) is in our set since all connected components have a single vertex, while
G = (N, E) with E = {(n,n+1) | n € N} is not since all vertices are in a single infinite connected
component.
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