FSM - Graph Theory summary

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
=