Give an example of a graph G with p(G) = 7 and c(G) = 3.

Expert Solution

p(G) denotes the number of vertices in a graph G.

c(G) denotes the number of connected components of graph G.

We have to find a graph such that number of vertices in a graph is 7 and number of connected components is 3.

Here I have given 3 such examples as follows.

1) Graph G with 7 vertices, 4 edges and 3 connected components. i.e. p(G) = 7 and c(G) = 3

Here one component is G₁ with 2 vertices and one edge, Second component is G₂ with 4 vertices and 3 edges and third component G₃ is only a vertex v₁.

2) Graph G with 7 vertices, 5 edges and 3 connected components. i.e. p(G) = 7 and c(G) = 3

Here one component is G₁ with 3 vertices and 3 edges, Second component is G₂ with 2 vertices and 2 edges and third component G₃ with 2 vertices and 2 edges.

3) Graph G with 7 vertices, 5 edges and 3 connected components. i.e. p(G) = 7 and c(G) = 3

Here one component is G₁ with a single vertex v₁, Second component is G₂ with also single vertex v₂ and third component G₃ with 5 vertices and 5 edges.

Colby Messinger answered 2 years ago

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