The image features two graphs, labeled \( G_1 = (V_1, E_1) \) and \( G_2 = (V_2, E_2) \).**Graph \( G_1 \):**- A connected graph with seven vertices: \( a, b, c, d, e, f, \) and \( g \).- The edges connect the vertices as follows: - \( a \) is connected to \( c, d, e, f, \) and \( g \). - \( b \) is connected to \( c, d, e, f, \) and \( g \).**Graph \( G_2 \):**- An unconnected graph with three vertices: \( x, y, \) and \( z \).- There are no edges connecting the vertices in this graph, indicating isolated points.This depiction illustrates the structural differences between a connected graph \( G_1 \) and a disconnected graph \( G_2 \). d) What is the total degree of \( G_1 \)?e) Which vertices are adjacent to vertex \( f \)?f) Find the connected components of \( G_1 \) and \( G_2 \).

Degree : to total number of incoming and out going edge ( in directed graph there is two type of degree indegree and outdegree but in non-directed graph we simply call degree) Connected component : Connected component is the set of vertices interconnected with some path. for G1 degree of a is 3 degree of b is 2 degree of c is 3 degree of d is 2 degree of e is 1 degree of f is 1 degree of g is 1 degree of h is 1 for G2 degree of x is 0 degree of y is 0 degree of z is 0 Connected component in G1 { { a , b , c , d } , { g , f } , { e , h } } -> 3 Connected component in G2 { { x } , { y } , { y } } -> 31. total degree = 14 2. node adjacent to f is g 3. i. total no. of connected component in G1 = 3 ii. total no. of connected component in G2 = 3

Answered: d) What is the total degree of G1? e)…

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d) What is the total degree of G1? e) Which vertices are adjacent to vertex f? f) Find the connected components of G1 and G2.

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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Concept explainers

Any Pair Segment

A line segment is the part of a line that is represented by a connection of two end points. It encompasses both ends of the line, as well as all points in between. The length of a line cannot be measured, but the length of a segment can be measured. If a line segment is bounded by two end points, it is called a closed line segment, whereas an open line segment does not have both endpoints. A line segment with a single endpoint is called half-open. A closed line segment contains every point on the line that exists between the two end points. For example, if L is a line, then AB is a line segment of line L where A and B are endpoints of the line segment.

Question

The image features two graphs, labeled \( G_1 = (V_1, E_1) \) and \( G_2 = (V_2, E_2) \).

**Graph \( G_1 \):**
- A connected graph with seven vertices: \( a, b, c, d, e, f, \) and \( g \).
- The edges connect the vertices as follows:
- \( a \) is connected to \( c, d, e, f, \) and \( g \).
- \( b \) is connected to \( c, d, e, f, \) and \( g \).

**Graph \( G_2 \):**
- An unconnected graph with three vertices: \( x, y, \) and \( z \).
- There are no edges connecting the vertices in this graph, indicating isolated points.

This depiction illustrates the structural differences between a connected graph \( G_1 \) and a disconnected graph \( G_2 \).

d) What is the total degree of \( G_1 \)?

e) Which vertices are adjacent to vertex \( f \)?

f) Find the connected components of \( G_1 \) and \( G_2 \).

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