Homework Help is Here – Start Your Trial Now!
Engineering
Computer Engineering
Bipartite graphs Consider the following graph G, edge set of G1 is E = {(v1, v5), (V1, v6), (v2, v3), (v2, V7), (v3, v5), (V4, V5), (v5, v7), (V6, V7)}. Graph G1 thus has n = |V|=7 vertices and m = |E| = 8 edges. (V, E). The vertex set of G1 is V = {v1, v2, V3, V4, V5, V6, V7}, and the %3D 5 3 Let A = {v1, v3, v4, v7} and B = {v2, v5, v6}. Observe that (1) A C V and B C V are subsets of V, (2) their union AUB = V contains all of the vertices in V, and (3) the intersection ANB= 0 is the empty set. Also observe that for every edge e e E, it holds that one of the endpoints of e is in A and the other endpoint is in B. We say that a graph G = (V, E) is bipartite if there exist subsets A C V and BC V such that AUB = V and ANB= 0, and for every edge in E, edge e has one endpoint in A and one endpoint in B. The graph G, given above is bipartite. 1. For each of the following four graphs, determine whether it is bipartite or not. Justify your answer.

Bipartite graphs Consider the following graph G, edge set of G1 is E = {(v1, v5), (V1, v6), (v2, v3), (v2, V7), (v3, v5), (V4, V5), (v5, v7), (V6, V7)}. Graph G1 thus has n = |V|=7 vertices and m = |E| = 8 edges. (V, E). The vertex set of G1 is V = {v1, v2, V3, V4, V5, V6, V7}, and the %3D 5 3 Let A = {v1, v3, v4, v7} and B = {v2, v5, v6}. Observe that (1) A C V and B C V are subsets of V, (2) their union AUB = V contains all of the vertices in V, and (3) the intersection ANB= 0 is the empty set. Also observe that for every edge e e E, it holds that one of the endpoints of e is in A and the other endpoint is in B. We say that a graph G = (V, E) is bipartite if there exist subsets A C V and BC V such that AUB = V and ANB= 0, and for every edge in E, edge e has one endpoint in A and one endpoint in B. The graph G, given above is bipartite. 1. For each of the following four graphs, determine whether it is bipartite or not. Justify your answer.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
See similar textbooks
icon
Related questions
Question

bipartitr graphs

Bipartite graphs Consider the following graph G¡ = (V, E). The vertex set of G1 is V = {v1, v2, V3, V4, V5, V6, V7}, and the edge set of G1 is E = {(v1, v5), (v1, v6), (v2, v3), (V2, v7), (v3, v5), (v4, v5), (V5, v7), (V6, V7)}. Graph G1 thus has n = |V|= 7 vertices and m = |E| = 8 edges. Let A = {v1, v3, V4, V7} and B = {v2, v5, v6}. Observe that (1) ACV and B C V are subsets of V, (2) their union AU B =V contains all of the vertices in V, and (3) the intersection AN B = Ø is the empty set. Also observe that for every edge e € E, it holds that one of the endpoints of e is in A and the other endpoint is in B. We say that a graph G = (V, E) is bipartite if there exist subsets A C V and B C V such that AUB = V and ANB=0, and for every edge in E, edge e has one endpoint in A and one endpoint in B. The graph G1 given above is bipartite. 1. For each of the following four graphs, determine whether it is bipartite or not. Justify your answer. 2. Show that if a graph G = (V, E) is bipartite, then it has at most n? edges if n is even, and at most |(n2 – 1) edges if n is odd. Here n = |V| is the number of vertices in G.
Transcribed Image Text:Bipartite graphs Consider the following graph G¡ = (V, E). The vertex set of G1 is V = {v1, v2, V3, V4, V5, V6, V7}, and the edge set of G1 is E = {(v1, v5), (v1, v6), (v2, v3), (V2, v7), (v3, v5), (v4, v5), (V5, v7), (V6, V7)}. Graph G1 thus has n = |V|= 7 vertices and m = |E| = 8 edges. Let A = {v1, v3, V4, V7} and B = {v2, v5, v6}. Observe that (1) ACV and B C V are subsets of V, (2) their union AU B =V contains all of the vertices in V, and (3) the intersection AN B = Ø is the empty set. Also observe that for every edge e € E, it holds that one of the endpoints of e is in A and the other endpoint is in B. We say that a graph G = (V, E) is bipartite if there exist subsets A C V and B C V such that AUB = V and ANB=0, and for every edge in E, edge e has one endpoint in A and one endpoint in B. The graph G1 given above is bipartite. 1. For each of the following four graphs, determine whether it is bipartite or not. Justify your answer. 2. Show that if a graph G = (V, E) is bipartite, then it has at most n? edges if n is even, and at most |(n2 – 1) edges if n is odd. Here n = |V| is the number of vertices in G.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Computer Networking: A Top-Down Approach (7th Edi…
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Concepts of Database Management
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY
SEE MORE TEXTBOOKS