Use assigned number of vertices (14) to do the following: Create a weighted connected graph with the following characteristics: • The assigned number of vertices (14) are alphabetically labeled starting with A. • Vertex A is not adjacent to vertex G. • At least two vertices have a degree greater than 2. • All weights are greater than 0. • No weights are the same. 1. Identify the degree of each vertex in your graph. 2. Explain whether the graph has an Euler trail, using definitions, properties, or theorems. 3. Describe a path from vertex A to G. 4. Find the total weight of the path from part F3. Show all work.

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A: a. Cheapest path from M to C. b. 2 examples where cheapest path is not the shortest path.

Q: 1 b. 3.

A: Adjacency Matrix   a b c d a 0 1 2 5 b 0 0 3 0 c 0 0 0 1 d 0 0 0 0

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A: Please refer to the following steps for the complete solution of the problem above.

Q: D) What is the size of the graph? E) Find the shortest path distance from vertex F to vertex D.

A: Size of the graph is number of edges in the graph

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A: