# Outerplanar Graphs

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A graph is outerplanar if it can be embedded in the plane so that every vertex lies on the boundary of the exterior region. Prove the following:

If G = G(p, q) is outerplanar with p >= 2, then q <= 2p - 3.

Â© BrainMass Inc. brainmass.com March 4, 2021, 8:11 pm ad1c9bdddfhttps://brainmass.com/math/graphs-and-functions/outerplanar-graphs-150387

#### Solution Preview

Proof. Note that the fact that G is outplanar if and only if H=G+K_1 is planar. You can prove it very easily.

Now consider the graph H=G+K_1. ...

#### Solution Summary

Outerplanar graphs are investigated. The solution is detailed and well presented.

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