Let G-(V,E), where V a, b, c,d,e,f.g,h and E- lla, b], [a,c), tb, c),{b,d), [b, g],...
File Edit Format View Help Graphs and trees 4. [6 marks] Using the following graph representation (G(V,E,w)): v a,b,c,d,e,f E fa,b), (a,f),fa,d), (b,e), (b,d), (c,f),(c,d),(d,e),d,f)) W(a,b) 4,W(a,f) 9,W(a,d) 10 W(b,e) 12,W(b,d) 7,W(c,d) 3 a) Draw the graph including weights. b) Given the following algorithm for Inding a minimum spanning tree for a graph: Given a graph (G(V,E)) create a new graph (F) with nodes (V) and no edges Add all the edges (E) to a set S and order them...
Let G -(V, E) be a graph. The complementary graph G of G has vertex set V. Two vertices are adjacent in G if and only if they are not adjacent in G. (a) For each of the following graphs, describe its complementary graph: (i) Km,.ni (i) W Are the resulting graphs connected? Justify your answers. (b) Describe the graph GUG. (c) If G is a simple graph with 15 edges and G has 13 edges, how many vertices does...
graph G, let Bi(G) max{IS|: SC V(G) and Vu, v E S, d(u, v) 2 i}, 10. (7 points) Given a where d(u, v) is the length of a shortest path between u and v. (a) (0.5 point) What is B1(G)? (b) (1.5 points) Let Pn be the path with n vertices. What is B;(Pn)? (c) (2 points) Show that if G is an n-vertex 3-regular graph, then B2(G) < . Further- more, find a 3-regular graph H such that...
Explain ur working 4. [6 marks] Using the following graph representation (G(VE,w)): V a, b,c, d,e, fh E -la, b, [a, fl,la,d, (b,ej, [b,d, c,fl,fc,d],Id,el, sd, f) W(a, b) 4, W(a, f)-9, W(a, d)-10 W(b, e) 12, W (b, d)7, W(c,d) 3 a) [3 marks] Draw the graph including weights. b) [2 + 1-3 marks] Given the following algorithm for finding a minimum spanning tree for a graph: Given a graph (G(V,E)) create a new graph (F) vith nodes (V)...
Linear Algebra 2) General Inner Products, Length, Distance and Angle a) Determine if (u,v)-3uiv,-u,v, is a dot product b) Show that (u.v)-a+a,h,'2 is a product if a, 20 e)Let A-(41 ..)and B-G ) Use inner product on 4 -2 M (A, B aitai +apb +2a to find the length of A, B, namely ll-41 and 1 d) Find the angle between the two matrices above e) Find the distance between the two above matrices 0) For the functions (x)-1 and...
The sample space of a random experiment is {a,b,c,d,e,g,h}. Let A denote the event {a,b,c,d,e,g,h}, and let B denote the event {c,d,e,g} The sample space of a random experiment is (a, b, c, d, e, g, h). Let A denote the event(a, b, c, e, g, h), and let B denote the event {c, d, e, g). (25 points) 3. Determine the following: (a) B, (c) A (d) AUB' (e) AnB (n A'nB'
Question 1 part a, d, e, f, g, h Construct and plot the network using the igraph package http://igraph.org/redirect.html and the adjacency list you wrote. To assign vertex names you can write it as g = graph(edges = c("a", "b", "b", "c"), directed = FALSE) or g = graph(edges = c(1, 2, 2, 3), directed = FALSE) V(g)$name = c("a", "b", "c") 1. Answer the following questions about this graph. a. What is the degree distribution for th graph? b....
Problem 6 (20 points). Let G- (V,E) be a directed Let E' be another set of edges on V with edge length '(e) >0 for any e EE. Let s,t EV. Design an algorithm runs in O(lV+ E) time to find an edge e'e E' whose addition to G will result in the maximum decrease of the distance from s to t. Explain why your algorithms runs in O(V2+E') time. graph with edge length l(e) >0 for any e E...
(1 point) Let a graph have vertices C, D, E, F, G, H and edge set {{C, D},{C, E}, {C, F}, {C, H},{D, E}, {D, F}, {D, G}, {F,G}}. a. What is the degistrerte 2 bow What is the degree of vedexOT c. How many components does the graph have? 2
Let (G, s, t, c) be a flow network G = (V, E), A directed edge e = (m u) is called always fu ir f(e) e(e) forall maximum fiows f: it is called sometimes fullit f(e)for some but not all maximum flows: it is caled never fulit f(e) <c(e) for all maximum flows. Let (S, V S be a cut. That is, s E S,teV S. We say the edge u, ) is crossing the cut ifu E SandrEV\...