Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
graph
|
| gptkbp:category |
extremal graph
|
| gptkbp:definedIn |
a regular graph of degree d and diameter k with the maximum possible number of vertices
|
| gptkbp:degree |
d
|
| gptkbp:diameter |
k
|
| gptkbp:example |
Hoffman–Singleton graph (for d=7, k=2)
Petersen graph (for d=3, k=2) complete graph (for k=1) cycle graph of length n (for d=2, k=n/2) |
| gptkbp:field |
gptkb:mathematics
graph theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Moore graph
|
| gptkbp:namedAfter |
gptkb:E._H._Moore
|
| gptkbp:nonExistence |
no Moore graphs for d>2, k>2 except for known cases
|
| gptkbp:openProblem |
existence for d=57, k=2 is unknown
|
| gptkbp:order |
1 + d + d(d-1) + ... + d(d-1)^{k-1}
|
| gptkbp:property |
regular graph
maximum number of vertices for given degree and diameter |
| gptkbp:relatedTo |
strongly regular graph
cage graph |
| gptkbp:bfsParent |
gptkb:graph
|
| gptkbp:bfsLayer |
5
|