Summary
FSM - Graph Theory summary
- Module
- Institution
Full, in detail, summary of all graph theory content needed for the final examination (Further Studies in Mathematics, Graph Theory and Matrices).
[Show more]
Seller
Follow
ricciwaksman
Reviews received
Content preview
GRAPH THEORY CGraph =Glany other capital letter)
Vertex (=v)
·
Number of vertices
Svertex set V)
=
=n =
Edge
·
= e) (lledges =
multiple edges btwn vertices
ledgesetEl
Degree (deg(v)
·
number of
edges vertex
=
on a
(degree sequence- list of degrees of all vertices in order)
Bridge edge to connect I isolated parts of a
graph
Classification
Simple - undirected
-> no
loops
-> no Il
edges
Regular -
all vertices have the same
degree
Connected - all vertices have a
degree >O Li . e . all connected in some way)
C... unconnected > I vertex has degree =Ob
complete -
every
vertex is joined to every other vertex
Complement /inverse of a
graph a inverse of G G
=
- same vertices edges missing from original graph
->
G +
a =
complete graph
formula
Degree sum works for undirected
graphs
E =
21E)
rev
I somorphic
isomorphic if
graphs have the SAME
graphs natare the same
I
graphs are
they - number of vertices
number of
->
edges
-> for corresponding vertices
degrees
-> number of connected components
↳number of lOOPs
Can be asked :
: ↳ number o f II edges
- To prove Graph 1 Graph 2
vertices if all
==> isomorphic
&
Edges if one I
list
=> not isomorphic
Degree
connected comp .
LOOPS
"I
edges
to make them isomorphic
-) what to add to one
graph
Graph families
(n) .. ....
edges
graph
=
no
Empty
Cyclegraphcan vertise" acaocion. zices of
graphsoznarnoz adjacent vertices nave the same
x((n)
E
=
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller ricciwaksman. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for £6.79. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
66579 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy revision notes and other study material for 14 years now