# MAT 230 Module 8 Homework.docx - 1 Draw a picture of the...

• emyatt0725
• 2
• 91% (11) 10 out of 11 people found this document helpful

This preview shows page 1 - 2 out of 2 pages.

1) Draw a picture of the graph G = (V, E, ) where V = {t, u, v, w, z}, E = {e 1 , e 2 , e 3 e 4 , e 5 }, and (e 1 ) = {v, w}, (e 2 ) = {t, u}, (e 3 ) = {t, v}, (e 4 ) = {u, w}, (e {t, w}. You may use (copy/paste/move/resize/etc.) the images below to create your graph. , 5 ) = 2) Consider Kn, the complete graph on n vertices. Explain how you calculated your answers. a) What is the degree of each vertex? Each vertex has a degree of (n – 1) because the vertices all must connect to each other. Example: If it had vertices {a, b, c, d, e, f, g} for a total of 7 vertices, “a” would need to connect to the other six {b, c, d, e, f, g} giving it a degree of six. b) How many edges does K n have? To determine the number of edges we can use a combination where we take n possible vertices and choose 2 to be assigned as the endpoints of the edges. This would be the formula n C 2 . Example: 5 C 2 3) Does the following graph have an Euler circuit, an Euler path, both, or neither? Give reasons for your decision. = 10