Q19D. Given the graph with the following vertices and edges:V = (a, b, c, d, e, f}E = {{a, b}, {a, e}, {b, c}, {b, f}, {d, e}, {e, f}}aebCHow many edges must be removed to form a spanning tree of the graph?A

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Answered: Q19D. Given the graph with the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let a graph have vertices O, P, Q, R, S, T, U, V and edge set{ { O,P} , {O,Q} , {O,S} {O,T} {Q,R} {Q,T} {Q,V} {R,S} {R,V} {T,U} }a. What is the degree of vertex ?b. What is the degree of vertex ?c. How many components does the graph have?
2. Draw a graph with the following vertex and edge sets: (a) V = {a,b, c, d, e, f} and E = {ac, ad, ba, eƒ, dc, de} %3D (b) V = {a, 8, 7, 4} and E = {ad, &y, yø, pa, p8, ya} %3D
Q17. Consider the graph with the following vertices, edges, and weights (weights are stated as the third entry for each edge in E, with the first two entries representing the vertices joined by the edge): V = {a, b, c, d, e, f, g} E = {{a, b, 10}, {a, c, 12}, {a, d, 15}, {a, f, 3}, {b, c, 11}, {b, e, 9}, {b, f, 7}, {c, d, 11}, {c, g, 15}, {d, e, 12}, {d, f, 10}, {f, g, 16}} b a Your Answer: d Answer CD e What is the total weight of a minimum spanning tree of the graph? g
Q15B. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f} E = {{a, b}, {a, e}, {b, c}, {b, f}, {d, e}, {e, f}} d a b D e (D Which of the following sets of edges represent subgraphs of the graph that are spanning trees? (Select all that apply.) {{a, b}, {a, e}, {b,c}} {{a, b}, {a, e}, {b,c}, {b, f}, {e, f}} {{a, b}, {b, c}, {d, e}, {e, f}} {{a, b}, {a, e}, {b, c}, {d, e}, {e, f}} C {{a, e}, {b, c}, {b, f}, {d, e}, {e, f}}
Draw these graphs. a) K1,4 b) W4
Q17. Consider the graph with the following vertices, edges, and weights (weights are stated as the third entry for each edge in E, with the first two entries representing the vertices joined by the edge): V = {a, b, c, d, e, f, g} E = {{a, b, 10}, {a, c, 12}, {a, d, 15}, {a, f, 5}, {b, c, 11}, {b, e, 9}, {b, f, 2}, {c, d, 11}, {c, g, 12}, {d, e, 12}, {d, f, 10}, {f, g, 16}} b a d e CD What is the total weight of a minimum spanning tree of the graph?
Consider the tree diagram. Path number 1 B1 C2 2 4 C2 4 4 4 B3 6 3 Find P(C,|B2) · P(B2). (Enter your answer as a fraction.)
Let a graph have vertices H, I, J, K, L, M and edge set TH,I}, {H, K},{I, J}, {I, L},{J, K}, {J, M}, {K, M}, {L, M}}. a. What is the degree of vertex H ? b. What is the degree of vertex J? c. How many components does the graph have?
2. A graph has vertices of degrees 0, 2, 2, 3, and 9. How many edges does the graph have?
H3.
Answer the following questions based on the given graph. B D. H Number of vertices of the given graph %3D Number of edges of the given graph= Is the above graph is a tree ? (Type either Yes or No)
If the simple graph G has v vertices and e edges, how many edges does the complement of G have? Ⓒa. none of the choices Ob. ve 2 O c. e² - 2e O d. v² v 2e Oe. e² 3e 2

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Q19D. Given the graph with the following vertices and edges: V = {a, b, c, d, e, f} E = {{a, b}, {a, e}, {b, c}, {b, f}, {d, e}, {e, f}} a b ⠀ How many edges must be removed to form a spanning tree of the graph? d C