Apply the proper Theorems and formulas to answer the following questions using the correct notations. 1) Is this a connected graph? Motivate your answer giving an exhaustive explanation. 2) Is this a complete graph? Motivate your answer giving an exhaustive explanation and if it is a complete graph calculate the number of edges applying the proper formula used for complete graphs. 3) Write the set of vertices of the graph and the set of the edges. Which is the number of vertices, and which is the number of edges in the graph? 4) Calculate the degree of each vertex. 5) Calculate the sum of the degrees of the vertices using the proper formula
Apply the proper Theorems and formulas to answer the following questions using the correct
notations.
1) Is this a connected graph? Motivate your answer giving an exhaustive explanation.
2) Is this a complete graph? Motivate your answer giving an exhaustive explanation and if it is a
complete graph calculate the number of edges applying the proper formula used for
complete graphs.
3) Write the set of vertices of the graph and the set of the edges. Which is the number of
vertices, and which is the number of edges in the graph?
4) Calculate the degree of each vertex.
5) Calculate the sum of the degrees of the vertices using the proper formula.
6) Does this graph have the Euler circuit? Motivate your answer giving an exhaustive
explanation and using Theorems to support your answer. If the Euler circuit exists, calculate
it, and write its path.
7) Does this graph have the Hamilton circuit? Motivate your answer giving an exhaustive
explanation and using Theorems to support your answer. If the Hamilton circuit exists,
calculate it, and write its path.
8) Calculate the minimum spanning tree applying the proper
and draw the tree.
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