Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    16
    ReputationRep:
    Can someone please explain this question a bit further and show me how they worked it out without using the same thing they did in the book Thank you.

    " Prove that there must always be an even (or zero) number of vertices with odd valency in every graph"

    Thank you ~ Noah.
    • Community Assistant
    Offline

    18
    ReputationRep:
    Community Assistant
    It's the handshaking lemma. Each arc contributes 2 to the valency, so the sum of the valencies must be even. So you can't have an odd number of nodes with odd valency; in that case the sum of the valencies would be odd.
    • Thread Starter
    Offline

    16
    ReputationRep:
    (Original post by NotNotBatman)
    It's the handshaking lemma. Each arc contributes 2 to the valency, so the sum of the valencies must be even. So you can't have an odd number of nodes with odd valency; in that case the sum of the valencies would be odd.
    So for the exam do I only really need to understand for hand shaking lemma that The total valency/degree is double the total arcs/edges ?
    • Community Assistant
    Offline

    18
    ReputationRep:
    Community Assistant
    (Original post by NoahMal)
    So for the exam do I only really need to understand for hand shaking lemma that The total valency/degree is double the total arcs/edges ?
    Yes.
 
 
 
Poll
Who is your favourite TV detective?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.