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FSM - Graph Theory summary
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Full, in detail, summary of all graph theory content needed for the final examination (Further Studies in Mathematics, Graph Theory and Matrices).
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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
=
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