11. Given:V = {1,2,3,4,5}E = {(1,2), (1,3), (1,4), (1,5), (2,4), (2,5), (3,4)}a) Draw the graph G (V, E)b) Is G (V, E) a complete graph? Why?c) Represent the graph with an adjacency matrix.

Answered: Image /qna-images/answer/8523bb72-1b01-4b1f-965d-08246148fdf9.jpg

Answered: 11. Given: V = {1,2,3,4,5) E = {(1,2),…

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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9.1 Explain whether a graph with each of the following characteristics exists. If so, give an example. If not, justify your answer. (a) A planar graph with 6 vertices, 10 edges and 5 faces. (b) A planar graph G with 6 vertices with degrees 2, 2, 3, 4, 4, 5. (c) A planar graph with 7 vertices, 10 edges and 4 faces. (d) A planar graph with 10 vertices and edges.
Determine whether the graph shown hasdirected or undirected edges, whether it has multiple edges,and whether it has one or more loops. Use your answers todetermine the type of graph in Table 1 this graph is.
-nsider the following graph G(V, E) w • The set of vertices V: {2,3, 4, 6, 8, • The set of edges E: {(a, b) e Z² : « a) Draw the graph G. b) Draw the graph G3
Consider the graph G with • V(G) = {2,3,6} • e(G) = {a, b, c, d, e, f, g} •E(G) = {(a, [2,2]), (b, [3,3]), (c, [6,6]), (d, [2,6]), (e, [6,2]), (f, [3,6]), (g, [6,3])} Using edge connectivity, we can define the relation R = {(2, 2), (3, 3), (6, 6), (2, 6), (6, 2), (3, 6), (6,3)} Which of the following statements are true? [More than one statement may be true.] R is reflexive. R is symmetric. R is transitive. R is antisymmetric.
if it is known that the graph has no direction G with the notation G = (V, E); V = (1, 2, 3, 4, 5, 6); E = (12, 14, 15, 23, 25, 26, 34, 36, 45, 46, 56) and there is a connected graph G' which is a subgraph of G which also has many vertices is 6 (| G'.V | = | GV |) and the minimal number of edges. a.how many G'(spanning tree)?
13. Draw the graph G(V, E) where V = (a, b, c, d, e, f) and E = {ab, ad, bc, cd, cf, de, df).
A Hamilton path of the graph K, is a (w, х, 2, у, t, у, z, 5) (x, W, S, z, t, y) (X, z, t, y, w, z, s) d (S, z, y, t, z, x, w) O000

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11. Given: V = {1,2,3,4,5) E = {(1,2), (1,3), (1,4), (1,5), (2,4), (2,5), (3,4)} a) Draw the graph G (V, E) b) Is G (V, E) a complete graph? Why? c) Represent the graph with an adjacency matrix.