4.1.6. (-) For a graph G with blocks B₁,..., Bk, prove that n(G) = (Σ₁n(B;)) − k +1.
4.1.6. (-) For a graph G with blocks B₁,..., Bk, prove that n(G) = (Σ₁n(B;)) − k +1.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Transcribed Image Text:BLOCKS
A connected graph with no cut-vertex need not be 2-connected, since it
can be K₁ or K₂. Connected subgraphs without cut-vertices provide a useful
decomposition of a graph.
4.1.16. Definition. A block of a graph G is a maximal connected subgraph of
G that has no cut-vertex. If G itself is connected and has no cut-vertex,
then G is a block.
Now answer the question 4.1.6
4.1.6. (-) For a graph G with blocks B₁,..., Bk, prove that n(G) = (₁ n(B₁)) - k +1.
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