Chapter 7.2, Problem 15E

Q10. What are the chromatic numbers of the following two graphs? G H A. x(G) = 2 and x(H) = 2 B. x(G) = 2 and x(H) = 3 C. x(G) = 3 and x(H) = 2 D. X(G) = 3 and x(H) = 3 E. x(G) = 4 and x(H) = 3

a/Let G be agraph. Then X (6) > 3 if and only if G has an odd.

Q/Let G be agraph with n vertices,n2 = then G has at least two vertices which are not cut vertices.

Q/ prove that :- For any graph GX (G) A (G) +1

Q/prove that:- An edge only if e e of agraph G is abridge if and is not part of any cycle in G.

Q/ Give an Such that L(G) example of a simple graph G is Euler but G is not.

Attempted the problem with different numbers but got a row of zeros and does not match the answer provided; even with the free variables. I dont know what I'm doing wrong

Let G be a graph with the following properties: G is simple, connected and planar. Every vertex of G has a degree of 4. Every face of G has three edges and every edge of G belongs to two faces. Does such a graph exist? If so, how many vertices, edges and faces does it have? (Hint: Turn each of the above property into an equation about the number of vertices, edges and/or faces of the graph.)

You are provided with data that includes all 50 states of the United States. Your task is to draw a sample of: o 20 States using Random Sampling (2 points: 1 for random number generation; 1 for random sample) o 10 States using Systematic Sampling (4 points: 1 for random numbers generation; 1 for random sample different from the previous answer; 1 for correct K value calculation table; 1 for correct sample drawn by using systematic sampling) (For systematic sampling, do not use the original data directly. Instead, first randomize the data, and then use the randomized dataset to draw your sample. Furthermore, do not use the random list previously generated, instead, generate a new random sample for this part. For more details, please see the snapshot provided at the end.) Upload a Microsoft Excel file with two separate sheets. One sheet provides random sampling while the other provides systematic sampling. Excel snapshots that can help you in organizing columns are provided on the next…