1. Draw your own graph with a. at least ten vertices, b. an edge with multiplicity...

Transcribed Image Text:

1. Draw your own graph with a. at least ten vertices, b. an edge with multiplicity three, C. at least three vertices that are all adjacent to each other, and d. a vertex with five neighbors. Draw this same graph again, but make sure that your second drawing has a different number of edge crossings than your first drawing. 2. Determine the degree of each vertex in the graph you just drew. Add up the numbers you get. How does this compare to the number of edges? 3. You now have four examples to work with: conjecture a relationship between the sum of the degrees of a graph (with a finite number of vertices) and the number of edges of that graph. Next, prove that your conjecture is correct. 4. Count the number of vertices of odd degree in each of the four graphs (including the one you created). For each graph, is the number even or odd? Make a conjecture about the number of vertices of odd degree a graph has. Can you prove it? 1. Draw your own graph with a. at least ten vertices, b. an edge with multiplicity three, C. at least three vertices that are all adjacent to each other, and d. a vertex with five neighbors. Draw this same graph again, but make sure that your second drawing has a different number of edge crossings than your first drawing. 2. Determine the degree of each vertex in the graph you just drew. Add up the numbers you get. How does this compare to the number of edges? 3. You now have four examples to work with: conjecture a relationship between the sum of the degrees of a graph (with a finite number of vertices) and the number of edges of that graph. Next, prove that your conjecture is correct. 4. Count the number of vertices of odd degree in each of the four graphs (including the one you created). For each graph, is the number even or odd? Make a conjecture about the number of vertices of odd degree a graph has. Can you prove it?