1. (a) Apply Kruskal's algorithm to find a minimal weight spanning tree and its weight for the graph on vertices v1, V2, V3, V4, V5, V6 with the following edges (and corresponding weights) edge: V3V5 V2V3 V3V6 V4 Vs V1V4 V1V2 V2 V6 V1V5 V3V5 weight: 9 3 8 5 2 4 7 1 Set out your answers in a table, as in Practice Class 9A (Questions 4 and 5). (b) Draw your spanning tree on the following set of vertices: V1 v2 V3 V4 V5 V6

Fundamentals of Information Systems
8th Edition
ISBN:9781305082168
Author:Ralph Stair, George Reynolds
Publisher:Ralph Stair, George Reynolds
Chapter3: Database Systems And Applications
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Problem 2.1DQ
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Assignments are designed to help you master concepts, solve problems and
develop your mathematical communication skills. Considerable weight is given
to the way you communicate your answers.
1. (a) Apply Kruskaľ's algorithm to find a minimal weight spanning tree
and its weight for the graph on vertices v1, v2, V3, V4, V5, V6 with the
following edges (and corresponding weights)
edge: V3V5 V2V3 V3V6 V4 V5 V1V4 V1V2 V2V6 V1V5 V3V5
weight: 9
Set out your answers in a table, as in Practice Class 9A (Questions 4
and 5).
6 3 8 5
2
4
7
1
(b) Draw your spanning tree on the following set of vertices:
v2
V3
V4
V5
V6
Step
N(1) N(2) N(3) N(4) N(5) N (6) N(7)
Edge set
Weight
Initially
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Step 8
1
2
3
4
6
7
{e1}
{e1,©2}
{e1, €2, €3}
{e1, ¢2, €3, e4}
{e1, @2, €3, €4, €5}
{e1, e2, €3, €4, €5}
{e1, ¢2, €3, €4, €5}
{e1,e2, €3, €4, €5, €s}
1
3.
4
5
6
3
1
1
4
5
3
3
1
2
3
1
1
5
3
10
1
1
1
1
5
1
15
1
5
1
15
1
1
1
1
15
1
1
1
1
1
1
1
23
The Question (a) use this form to do
Transcribed Image Text:Assignments are designed to help you master concepts, solve problems and develop your mathematical communication skills. Considerable weight is given to the way you communicate your answers. 1. (a) Apply Kruskaľ's algorithm to find a minimal weight spanning tree and its weight for the graph on vertices v1, v2, V3, V4, V5, V6 with the following edges (and corresponding weights) edge: V3V5 V2V3 V3V6 V4 V5 V1V4 V1V2 V2V6 V1V5 V3V5 weight: 9 Set out your answers in a table, as in Practice Class 9A (Questions 4 and 5). 6 3 8 5 2 4 7 1 (b) Draw your spanning tree on the following set of vertices: v2 V3 V4 V5 V6 Step N(1) N(2) N(3) N(4) N(5) N (6) N(7) Edge set Weight Initially Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 1 2 3 4 6 7 {e1} {e1,©2} {e1, €2, €3} {e1, ¢2, €3, e4} {e1, @2, €3, €4, €5} {e1, e2, €3, €4, €5} {e1, ¢2, €3, €4, €5} {e1,e2, €3, €4, €5, €s} 1 3. 4 5 6 3 1 1 4 5 3 3 1 2 3 1 1 5 3 10 1 1 1 1 5 1 15 1 5 1 15 1 1 1 1 15 1 1 1 1 1 1 1 23 The Question (a) use this form to do
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