The graph G shown below is the union of three connected components G1,G2,G3.(The graph G consists of the three connected components G1, G2 and G3.)
(1)what is Chromatic numberχ(G)
(2)what is Chromatic polynomialρG(k) (do not expand).
(3)what is the number of 6-colorings of G. (No need to simplify
the answer.)
Homework Answers
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The graph G shown below is the union of three connected
components G1,G2,G3.(The graph G consists...
1) Consider the directed graph below. “S” is the start state and “G1,G2,G3” are 3 goal...
1) Consider the directed graph below. “S” is the start state and “G1,G2,G3” are 3 goal states. In traversing the graph one can move only in the direction indicated by the arrows. The numbers on the edges indicate the step-cost for traversing that edge. The numbers in the nodes represent the estimated cost to the nearest goal state. In the following you will be asked to search this graph using various search strategies. When you work out your answer, please...
6. Prove that the following graphs are connected: (a) The 3 vertex cycle: (b) The following 4 vertex graph: (c) K 7. An edge e of a connected graph G is called a cut edge if the graph G obtained by d...
6. Prove that the following graphs are connected: (a) The 3 vertex cycle: (b) The following 4 vertex graph: (c) K 7. An edge e of a connected graph G is called a cut edge if the graph G obtained by deleting that edge (V(G) V(G) and E(G) E(G) \<ej) is not connected. Prove that if G1 and G2 are connected simple graphs which are isomorphic and if G1 has a cut edge, then G2 also has a cut edge....
19. Use the definition below and the minimum criteria a graph must meet in order to be potentially isomorphic to answer the question Recall Definition: Isomorphism: For a graph G1 V, E13 and G2-V2, E...
19. Use the definition below and the minimum criteria a graph must meet in order to be potentially isomorphic to answer the question Recall Definition: Isomorphism: For a graph G1 V, E13 and G2-V2, E23 G1is isomorphic to G2 denoted GG2 iff af:V V2where i) f is bijective and Describe an isomorphism between the following two graphs, or briefly explain why no such isomorphism exists. f(A)1 f(B)6 f(C) 3 f(D)8 IG)2 f(H)5 f(I)4
19. Use the definition below and the...
A system consists of five components is connected in series as shown below. -1 42 43...
A system consists of five components is connected in series as shown below. -1 42 43 44 45 As soon as one component fails, the entire system will fail. Assume that the components fail independently of one another. (a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 107 weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean 136 weeks. Find the probability that the...
Problem 3 (15 points) Consider the graph shown on the right. Find the strongly connected componen...
Problem 3 (15 points) Consider the graph shown on the right. Find the strongly connected components of the graph. For full credit, a) (6 points) Run DFS on the reverse graph, showing the discovery and finish times of each 10 vertex. b) (6 points) Run DFS again, to discover the strongly connected components. What is the 15 order the components are discovered? 12 c) (3 points) Draw the DAG of the components. What is the minimum number of edges that...
QUESTION 2. (a) A portion of a power system consists of two generators in parallel, connected...
QUESTION 2. (a) A portion of a power system consists of two generators in parallel, connected to a step-up transformer that links them with a 220-kV transmission line. The ratings of these components are as shown below: Generator GI: 10 MVA, 12 percent reactance Generator G2: 5 MVA, 8 percent reactance Transformer: 15 MVA, 6 percent reactance Transmission line: (4+j60) 22, 220kV where the percent reactances are computed on the basis of individual component ratings. Draw the per-unit impedance diagram...
G1: I can create a graph given information or rules about vertices and edges. I can...
G1: I can create a graph given information or rules about vertices and edges. I can give examples of graphs having combinations of various properties and examples of graphs of special (" named”) types. 1. Draw a graph G with • V(G) = {a,b,c,d,e,f}, • deg(d) = 2, • a and f are neighbors, • {b,d} & E(G), G is simple, • K4 is a subgraph of G. 2. Draw the graph C7. 3. Answer each question about the graph...
QUESTION 1 In the circuit shown below a three-phase, three-wire, Y-connected power system is driving a...
QUESTION 1 In the circuit shown below a three-phase, three-wire, Y-connected power system is driving a A-connected load. The generator line-to-line voltages are 150 V. The impedance of each phase of the load consists of a 6- resistance and a 8-inductive reactance. Determine the magnitude of the line current IA (in A). (Enter your answer as a decimal number without the units.) 3a, 3 wire Y-winacted generator Pane e ABC B! 150 V20
ignore red marks. Thanks 10. (16) You will compute the strongly connected components of this graph...
ignore red marks. Thanks
10. (16) You will compute the strongly connected components of this graph in three steps. a. STRONGLY-CONNECTED-COMPONENTS (G) (7) Perform a depth-first search on call DFS(G) to compute finishing times w/ for each vertex the following graph. (To make 2 compute GT this easier to grade, everyone call DFS(GT), but in the main loop of DFS, consider the vertices in order of decreasing wf (as computed in line 1) please start with vertex "a" and 4...
part B 1. The apparatus shown below consists of three 1.00L bulbs connected by stopcocks and...
part B
1. The apparatus shown below consists of three 1.00L bulbs connected by stopcocks and held at the temperatures shown. Bulb A contains a mixture of H2O, CO2, and N2 at 25°C and a total pressure of 564 mmHg. Bulbs B and C are empty. CO2 sublimes at -78°C and N2 boils at -196°C 25 °C -70。 -190 °C a. The stopcock between A and B is opened. The pressure in A and B is now 219 mmlHg. What...
6. Prove that the following graphs are connected: (a) The 3 vertex cycle: (b) The following 4 vertex graph: (c) K 7. An edge e of a connected graph G is called a cut edge if the graph G obtained by deleting that edge (V(G) V(G) and E(G) E(G) \<ej) is not connected. Prove that if G1 and G2 are connected simple graphs which are isomorphic and if G1 has a cut edge, then G2 also has a cut edge....
19. Use the definition below and the minimum criteria a graph must meet in order to be potentially isomorphic to answer the question Recall Definition: Isomorphism: For a graph G1 V, E13 and G2-V2, E23 G1is isomorphic to G2 denoted GG2 iff af:V V2where i) f is bijective and Describe an isomorphism between the following two graphs, or briefly explain why no such isomorphism exists. f(A)1 f(B)6 f(C) 3 f(D)8 IG)2 f(H)5 f(I)4
19. Use the definition below and the...
A system consists of five components is connected in series as shown below. -1 42 43 44 45 As soon as one component fails, the entire system will fail. Assume that the components fail independently of one another. (a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 107 weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean 136 weeks. Find the probability that the...
Problem 3 (15 points) Consider the graph shown on the right. Find the strongly connected components of the graph. For full credit, a) (6 points) Run DFS on the reverse graph, showing the discovery and finish times of each 10 vertex. b) (6 points) Run DFS again, to discover the strongly connected components. What is the 15 order the components are discovered? 12 c) (3 points) Draw the DAG of the components. What is the minimum number of edges that...
QUESTION 2. (a) A portion of a power system consists of two generators in parallel, connected to a step-up transformer that links them with a 220-kV transmission line. The ratings of these components are as shown below: Generator GI: 10 MVA, 12 percent reactance Generator G2: 5 MVA, 8 percent reactance Transformer: 15 MVA, 6 percent reactance Transmission line: (4+j60) 22, 220kV where the percent reactances are computed on the basis of individual component ratings. Draw the per-unit impedance diagram...
G1: I can create a graph given information or rules about vertices and edges. I can give examples of graphs having combinations of various properties and examples of graphs of special (" named”) types. 1. Draw a graph G with • V(G) = {a,b,c,d,e,f}, • deg(d) = 2, • a and f are neighbors, • {b,d} & E(G), G is simple, • K4 is a subgraph of G. 2. Draw the graph C7. 3. Answer each question about the graph...
QUESTION 1 In the circuit shown below a three-phase, three-wire, Y-connected power system is driving a A-connected load. The generator line-to-line voltages are 150 V. The impedance of each phase of the load consists of a 6- resistance and a 8-inductive reactance. Determine the magnitude of the line current IA (in A). (Enter your answer as a decimal number without the units.) 3a, 3 wire Y-winacted generator Pane e ABC B! 150 V20
ignore red marks. Thanks
10. (16) You will compute the strongly connected components of this graph in three steps. a. STRONGLY-CONNECTED-COMPONENTS (G) (7) Perform a depth-first search on call DFS(G) to compute finishing times w/ for each vertex the following graph. (To make 2 compute GT this easier to grade, everyone call DFS(GT), but in the main loop of DFS, consider the vertices in order of decreasing wf (as computed in line 1) please start with vertex "a" and 4...
part B
1. The apparatus shown below consists of three 1.00L bulbs connected by stopcocks and held at the temperatures shown. Bulb A contains a mixture of H2O, CO2, and N2 at 25°C and a total pressure of 564 mmHg. Bulbs B and C are empty. CO2 sublimes at -78°C and N2 boils at -196°C 25 °C -70。 -190 °C a. The stopcock between A and B is opened. The pressure in A and B is now 219 mmlHg. What...
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