Final answer:
A cubic graph with 2n vertices for some n≥3 and no triangles can be represented by a complete bipartite graph, where each vertex in one set is connected to every vertex in the other set.
Step-by-step explanation:
A cubic graph with 2n vertices for some n≥3 which has no triangles can be represented by a complete bipartite graph. A complete bipartite graph is a graph in which the vertices can be divided into two sets, V1 and V2, such that each vertex in set V1 is connected to every vertex in set V2. In this case, we can divide the 2n vertices into two sets of n vertices each, and connect each vertex in set V1 to every vertex in set V2.
This can be illustrated with an example. Let's say n=3, then we have 2n=6 vertices. We can divide these vertices into two sets V1 and V2, with V1={1,2,3} and V2={4,5,6}. Now, we connect every vertex in set V1 to every vertex in set V2, resulting in a graph with no triangles.
Here is how the graph looks like:
1 - 4
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2 - 5
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3 - 6