Johnson Graphs

​
set size
v
5
subset size
k
2
intersection size
i
0
label vertices
Explore the families of Johnson graphs, or explore the families of Kneser graphs by letting
i=0
.

Details

As defined by Godsil & Royle's Algebraic Graph Theory, let
v
,
k
, and
i
be fixed positive integers, with
v≥k≥i
; let
Ω
be a fixed set of size
v
; and define
J(v,k,i)
as follows: the vertices of
J(v,k,i)
are the subsets of
Ω
with size
k
. Two subsets are connected by an edge if their intersection has size
i
.

External Links

Kneser Graph (Wolfram MathWorld)
Johnson Graph (Wolfram MathWorld)
Kneser Graphs

Permanent Citation

Gustavo Gordillo
​
​"Johnson Graphs"​
​http://demonstrations.wolfram.com/JohnsonGraphs/​
​Wolfram Demonstrations Project​
​Published: January 18, 2012