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H(8,4) Hamming Graph

The Second DIMACS Implementation Challenge: 1992-1993

Originator: Panos Pardalos

NP Hard Problems: Maximum Clique, Graph Coloring, and Satisfiability, The Second DIMACS Implementation Challenge: 1992-1993.

A Hamming graph with parameters n and d has a node for each binary vector of length n. Two nodes are adjacent if and only if the corresponding bit vectors are hamming distance at least d apart.

Examples

Basic Examples

Retrieve the graph:

In[1]:=
ResourceData["H(8,4) Hamming Graph"]
Out[1]=

Summary properties:

In[2]:=
ResourceData["H(8,4) Hamming Graph", All]["Summary"]
Out[2]=

Basic Applications

Find the maximum clique:

In[3]:=
g = ResourceData["H(8,4) Hamming Graph"];
In[4]:=
maxclique = FindClique[g]
Out[8]=

Show the maximum clique:

In[9]:=
HighlightGraph[g, Subgraph[g, maxclique], VertexCoordinates -> ReplacePart[
GraphEmbedding[g, "SpringElectricalEmbedding"], 
Thread[Map[VertexIndex[g, #]& , 
First[maxclique]] -> CirclePoints[{3, 0.9}, 0.7, 
Length[
First[maxclique]]]]], Sequence[
 EdgeStyle -> {Blank[] -> Opacity[0.05]}, GraphLayout -> "SpringElectricalEmbedding", VertexSize -> {Blank[] -> 0.5}]]
Out[16]=

Wolfram Research, "H(8,4) Hamming Graph" from the Wolfram Data Repository (2019) 

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