BLOCKSA connected graph with no cut-vertex need not be 2-connected, since itcan be K₁ or K₂. Connected subgraphs without cut-vertices provide a usefuldecomposition of a graph.4.1.16. Definition. A block of a graph G is a maximal connected subgraph ofG that has no cut-vertex. If G itself is connected and has no cut-vertex,then G is a block.Now answer the question 4.1.64.1.6. (-) For a graph G with blocks B₁,..., Bk, prove that n(G) = (₁ n(B₁)) - k +1.

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Answered: 4.1.6. (-) For a graph G with blocks…

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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

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Concept explainers

Strongly Connected Components

A directed graph in which a path exists between all its pairs of vertices is called a strongly connected graph. A portion of the strongly connected directed graph that contains a path to reach from each vertex to other vertices is called a strongly connected component (SCC).

Question

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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