Ambassadors from countries A, B, C, D, E, and F are to be seated around a circular conference table. Friendly relations among the various countries are described as follows: A has friendly relations with B and F. B has friendly relations with A, C, and E. C has friendly relations with B, D, E, and F. E has friendly relations with B, C, D, and F. All friendly relations are mutual. Using vertices to represent countries and edges to represent friendly relations, draw a graph that models the information given. Then use a Hamilton circuit to devise a seating arrangement around the table so that the ambassadors from B and E are seated next to each other, and each ambassador represents a country that has friendly relations with the countries represented by the ambassadors next to him or her.
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EBK THINKING MATHEMATICALLY
- 1. Please look at the picture carefully and find the answer from multiple choice.arrow_forwardLet a graph have vertices S, T, U, V, W, X, Y and edge set {{S, V}, {S, X}, {U, W}, {U,X}, {V,X},{V,Y}, {X, Y}} a. What is the degree of vertex W ? b. What is the degree of vertex U? c. How many components does the graph have?arrow_forwardQ14C. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f, g} E = {{a, b}, {a, c}, {a, d}, {a, f}, {b, c)}, {b, e}, {b, f}, {c, d}, {c, g}, {d, e}, {d, f}, {f, g}} b a d e (1) g Which of the following sets of edges represent subgraphs of the graph that are trees? (Select all that apply.) {{a, b}, {a, c}, {a, d}} {[a, b}, {a, c}, {a, f}, {b, f}, {d, e}, {f, g}} |{{a, c}, {a, f}, {b, e}, {b, f}, {d, f}, {f, g}} {{a, b}, {b, c}, {a, f}, {c, d}, {d, e}, {f, g}} {{a, c}, {a, f}, {b, c}, {c, d}, {c, g}, {d, e}}arrow_forward
- The floor plan of a five-room house is shown. The rooms are labeled A, B, C, D, and E. The outside of the house is labeled F. The openings represent doors. Use the floor plan to answer the questions below. A B E a. Draw a graph that models the connecting relationships in each floor plan. Use vertices to represent the rooms and the outside, and edges to represent the connecting doors. Choose the correct answer below. A F А C В A D В E D В B D E D E F Yes - a path exists No such path exists DA BFCE Drag the correct answer into the target below, then, if a path exists, drag the vertex labels to the appropriate locations in the path. b. Use your graph to determine if it is possible to find a path that uses each door only once. c. If such a path exists, find one. If a path exists, it goes from F to B to E to to to to toarrow_forwardWhere are the vertices?arrow_forwardFind All vertices that are adjacent to v1. O v4 O v2, v1, v3 V5 O e1,e2, e7 O v5, v2 O e6 v1, v2, v3, v5 e 1 VI es e2 e5 • V4 e7 e 3. V2 e6 V3arrow_forward
- 3.) The graph below represents the chocolate consumed by people. a.) What is the constant of proportionality? 30 24 18 12 6 3 6. Реople 12 15 b.) What does the point (9,18) represent? Chocolatesarrow_forwardQ10B. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f, g} E = {{a, b}, {a, c}, {a, f}, {b, c}, {b, f}, {c, d}, {c, g}, {d, e}, {d, f}, {f, g}} a C d e g Which of the following are examples of circuits within the graph? (Select all that apply.)arrow_forwardDiscrete matharrow_forward
- Q10D. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f, g} E = {{a, b}, {a, c}, {a, d}, {a, f}, {b, c}, {b, e}, {b, f}, {c, d}, {c, g}, {d, e}, {d, f}, {f, g}} Which of the following are examples of circuits within the graph? (Select all that apply.) Question 10 options: < e, d, f, g, c > < b, c, a, b > < a, b, c, g, f, d > < a, c, f, a > < b, f, d, a, b >arrow_forwardG2. Draw a graph with the set of vertices V = {a, b, c, d} and the set of edges E= {{b, c), {c, d), (a, d}}. Find the degree of vertex a.arrow_forward3. Travel Nicole wants to tour Asia. She will start and end her journey in Tokyo and visit HongKong, Bangkok, Seoul, and Beijing. The airfares available to her betweencities are given in the table. Draw a weighted graph that represents the travel costs between cities and use thealgorithm to find a low-cost route. Highlight/color the edges to show the circuit.arrow_forward
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