Your question:

G = C5[2; 2; 2; 2; 2]. Find Θ(G) (the thickness of G) and prove that your answer is correct.

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Assignment Help Answers with Step-by-Step Explanation:

To find the thickness of a graph G, we need to determine the minimum number of edge-disjoint paths between any two vertices in the graph such that these paths do not share any common edges. In other words, we want to find the smallest number of paths required to disconnect the graph when we remove those paths.

In our case, G is an even-sized cycle (C5), so the thickness is 2.

Proof:

If we select two adjacent vertices, say vertex 1 and vertex 2, there are still two edge-disjoint paths between them. One path goes through the edge connecting vertex 1 and vertex 2, while the other path can be found by going clockwise or counterclockwise around the cycle, avoiding the direct edge.

In both cases, we have demonstrated that there are always two edge-disjoint paths between any pair of vertices in G. Therefore, the thickness of G is indeed 2, as calculated earlier.