..., Vn} Let G be an undirected, connected graph with vertex set V(G) = {v₁, v₂, ..., and edge set E(G) = {e₁,e2, ..., em }. Let B(G) = [bij] be an n × m matrix in which the (i, j)-th element bij = 1 if v; is one of the end vertices of e; and 0 otherwise. Fill in the blanks below. If it is a True-or-False type question, place a T or F, respectively. 1. The number of 1s in each column of B(G) is the same. True of False? 2. The number of 1s in row i is equal to the degree of edge i. 3. The total number of 1s in B(G) is

Database System Concepts
7th Edition
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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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4. Graphs represented in Matrix

Let G be an undirected, connected graph with vertex set V(G) = {V1, V2, ..., Vn}
and edge set E(G) = {e₁,e2,..., em}.
Let B(G) = [bj] be an n × m matrix in which the (i, j)-th element b¿j = 1 if v; is
one of the end vertices of e; and 0 otherwise.
Fill in the blanks below. If it is a True-or-False type question, place a T or F,
respectively.
1. The number of 1s in each column of B(G) is the same. True of False?
2. The number of 1s in row i is equal to the degree of edge i.
3. The total number of 1s in B(G) is
Transcribed Image Text:Let G be an undirected, connected graph with vertex set V(G) = {V1, V2, ..., Vn} and edge set E(G) = {e₁,e2,..., em}. Let B(G) = [bj] be an n × m matrix in which the (i, j)-th element b¿j = 1 if v; is one of the end vertices of e; and 0 otherwise. Fill in the blanks below. If it is a True-or-False type question, place a T or F, respectively. 1. The number of 1s in each column of B(G) is the same. True of False? 2. The number of 1s in row i is equal to the degree of edge i. 3. The total number of 1s in B(G) is
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