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Let B = {1,2,3}. We construct a graph G = (V, E) on n = 6 vertices with vertex set V = P(B)\{0, B}. Tha is, v € V is a vertex in G if v is a non-empty strict subset of B. There is thus no vertex in G that correspond to the empty set Ø, and there is no vertex in G that corresponds to the universe set B. The pair (u, v) is a edge in G if u Uv = B, that is, if the union of the two subsets u and v is B. 1. Draw G. Explain your construction. Give a clear drawing of G that is easy to read. 2. Give the adjacency matrix Adj(G) of G. Briefly explain.

Let B = {1,2,3}. We construct a graph G = (V, E) on n = 6 vertices with vertex set V = P(B)\{0, B}. Tha is, v € V is a vertex in G if v is a non-empty strict subset of B. There is thus no vertex in G that correspond to the empty set Ø, and there is no vertex in G that corresponds to the universe set B. The pair (u, v) is a edge in G if u Uv = B, that is, if the union of the two subsets u and v is B. 1. Draw G. Explain your construction. Give a clear drawing of G that is easy to read. 2. Give the adjacency matrix Adj(G) of G. Briefly explain.

Advanced Engineering Mathematics
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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graphs on subset

 

Graph on subsets Let B = {1,2,3}. We construct a graph G = (V, E) on n = 6 vertices with vertex set V = P(B)\{0,B}. That is, v e V is a vertex in G if v is a non-empty strict subset of B. There is thus no vertex in G that corresponds to the empty set 0, and there is no vertex in G that corresponds to the universe set B. The pair (u, v) is an edge in G if u U v = B, that is, if the union of the two subsets u and v is B. 1. Draw G. Explain your construction. Give a clear drawing of G that is easy to read. 2. Give the adjacency matrix Adj(G) of G. Briefly explain.
Transcribed Image Text:Graph on subsets Let B = {1,2,3}. We construct a graph G = (V, E) on n = 6 vertices with vertex set V = P(B)\{0,B}. That is, v e V is a vertex in G if v is a non-empty strict subset of B. There is thus no vertex in G that corresponds to the empty set 0, and there is no vertex in G that corresponds to the universe set B. The pair (u, v) is an edge in G if u U v = B, that is, if the union of the two subsets u and v is B. 1. Draw G. Explain your construction. Give a clear drawing of G that is easy to read. 2. Give the adjacency matrix Adj(G) of G. Briefly explain.
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