Let a graph have vertices K, L, M, N, O, P, Q, R and edge set{{L, M}, {L, O}, {L, P}, {L, R}, {M, N}, {M, R}, {N, P}, {P, R}, {Q, R}} .a. What is the degree of vertex O?b. What is the degree of vertex M?c. How many components does the graph have?

Given that a graph have vertices and following edge set..We need to find the degree of vertices .We…

Answered: Let a graph have vertices K, L, M, N,…

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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5. Consider the undirected graph G = {V, E}, where V, the set of nodes, is {1,2,3,4} and E, the set of edges, is {{1, 2}, {2,3}, {1,3}, {2,4}, {1,4}}. Draw the graph G. What is the degree of each node? Indicate on your drawing of G a path from node 3 to node 4 that uses three edges (has length 3).
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}}
Question 4. Let K, be the complete graph on n vertices. How many edges does it have? Justify your answer.
Draw these graphs. a) K1,4 b) W4
1. What is the largest n such that P₁, is a subgraph of K? 2. What is the largest n such that C₁ is a subgraph of K? 3. What is the largest n such that P₁ is an induced subgraph of K₁² 4. What is the largest n such that C₁ is an induced subgraph of K6?
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?
Previo Construct a connected simple graph, that has no circuit, with vertices M, N, 0, P, Q, R, S, T, U such that the degree of O is 4.

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Let a graph have vertices K, L, M, N, O, P, Q, R and edge set {{L, M}, {L, O}, {L, P), (L, R}, {M, N}, {M, R}, {N, P}, {P, R}, {Q, R}}. a. What is the degree of vertex O? b. What is the degree of vertex M? c. How many components does the graph have?