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Graph, Tree, Trail

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1. Determine if the attached graph is a tree. Please refer to Q1 in the attached Trees.pdf for the graph.

2. As few trails as possible, are to be built between houses in a primitive community so that it is possible for a resident to go from any house to any other. If there are 34 houses, how many trails need to be built?

Since it is considered bad luck to live at the end of a trail, can the trails be constructed so that no house is so situated?

3. Create a graph identical to the graph in Q3 in attached Trees.pdf, in a format that allows editing the graph easily.

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Solution Summary

Answers are well justified, and answer to primitive community question is explained in detail. The expert creates a graph for identical trees.

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1. Given graph can not be a tree because it contains a cycle.

2. Since a resident should be able to go from any house to any other following the trails, it means that we will need minimum 33 trails to connect 34 ...

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