5. For a chess piece Q, the Q-graph is the graph whose vertices are the squares of the chess board and the two squares are adjacent if Q can move from one of them to the other in one move. Find the chromatic number of the Q-graph when Q is (a) the king, (b) a rook, (c) a bishop, (d) a knight.

Q: Does this have 12 vertices? If not, how does that change the drawing and answers?

A: IntroductionGraph: A graph is a visual representation of edges and vertices, or dots and lines.A…

Q: What is the chromatic number of the graph K33, the graph with 33 vertices each connected to each…

A: We have graph K33 with 33 vertices connected to each other. So, we have a complete graph K33

Q: 2.) Determine how many backtracks are required to use every edge at least once returning to where…

A:

Q: 1. Consider the given graph. (a) Determine the number of vertices of the graph. (b) Determine…

A:

Q: What is the smallest number of colors you need to properly color the vertices of K3.3 ? That is,…

A:

Q: 4 1. -7 -6 -5-43 -2 -1, 1 2 3 4 5 6 78 -2 -3 -4 -5 -6 -7 -8 Co 3.

A: We have to find

Q: number

A:

Q: When n = 3, there are nonisomorphic simple graphs.

A:

Q: 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Option 1 Option 2 +++ 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Option 3…

A: X>4

Q: Prove that the two graphs below are isomorphic. Figure 4: Two undirected graphs. Each graph has 6…

A: Given,  We will prove these two graphs are isomorphic.

Q: Give an example of a tree with 6 vertices whose degrees are 1, 1, 1, 2, 2, and 3. Choose the correct…

A: Graph: A graph is defined as G = (V, E) Where V is a set of all vertices and E is a set of all edges…

Q: Construct a graph with vertices R,S,T,U whose degrees are 0,0,1,1. What is the edge set?

A:

Q: A simple connected graph with 2,024 vertices is such that there are exactly two vertices, u and v,…

A:

Q: (a) Color the graph below. That is, using the smallest number of colors possible, color the vertices…

A: Now we have the given graph First, we will start at A, and fill it with the first color violet. Then…

Q: Construct a graph with vertices A, B, C, D, E whose degrees are 1, 1, 1, 0, 1 What is the edge set?

A: