To determine If a graph contains a circuit that starts and ends at a vertex v, does the graph contain a simple circuit that starts and ends at v? Why?

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
icon
Related questions
Question
100%

Could you please explain the soltion in an easier way?

Expert Solution
To determine
If a graph contains a circuit that starts and ends at a vertex v, does
the graph contain a simple circuit that starts and ends at v? Why?
Answer to Problem 48ES
Yes
Explanation of Solution
Given information: A graph contains a circuit that starts and ends
at a vertex v.
Calculation:
Let vejvjezv.v-Je,v be a circuit that starts and ends at vertex v in
some graph G (for some positive integer n ).
If the circuit vejvje2v2..Vn–1enV contains no repeated vertices, then
the circuit vej vie2v2...Vn–1Env is a simple circuit as well.
If vejvjezv2..Vn-1enV contains some repeated vertex
Vị = vị (1 < ij <n- 1 with i + j), then we remove the part of the
circuit between these two vertices. the resulting path will still be a
circuit, because the circuit will still contain at least one edge and
will still contain no repeated edges. repeat this procedure until the
resulting circuit contains no more repeated vertex and the
resulting circuit then is a simple circuit.
We then note that the graph needs to contain a simple circuit that
starts and ends at v.
Vi+1
.....
Vn-1
Vi+1
Transcribed Image Text:Expert Solution To determine If a graph contains a circuit that starts and ends at a vertex v, does the graph contain a simple circuit that starts and ends at v? Why? Answer to Problem 48ES Yes Explanation of Solution Given information: A graph contains a circuit that starts and ends at a vertex v. Calculation: Let vejvjezv.v-Je,v be a circuit that starts and ends at vertex v in some graph G (for some positive integer n ). If the circuit vejvje2v2..Vn–1enV contains no repeated vertices, then the circuit vej vie2v2...Vn–1Env is a simple circuit as well. If vejvjezv2..Vn-1enV contains some repeated vertex Vị = vị (1 < ij <n- 1 with i + j), then we remove the part of the circuit between these two vertices. the resulting path will still be a circuit, because the circuit will still contain at least one edge and will still contain no repeated edges. repeat this procedure until the resulting circuit contains no more repeated vertex and the resulting circuit then is a simple circuit. We then note that the graph needs to contain a simple circuit that starts and ends at v. Vi+1 ..... Vn-1 Vi+1
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Knowledge Booster
Fundamentals of Boolean Algebra and Digital Logics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education