Pasechnik Graph

Author

Eric W. Weisstein
April 16, 2021

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/PasechnikGraph.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/PasechnikGraph.html.

©2021 Wolfram Research, Inc. except for portions noted otherwise

Source

Pasechnik, D. V.  "Skew-symmetric association schemes with two classes and strongly regular graphs of type (Subscript[L, 2n-1])(4n-1)."  Acta Applicandaie Math. 29, 129–138, 1992. doi:10.1007/BF00053382.

Graphs

DeleteCases[Show[GraphData[#],PlotLabel->GraphData[#,"Name"]]&/@With[{class="Pasechnik"},Sort[{Lookup[GraphData[#,"NotationRules"],class],#}&/@GraphData[class]][[All,2]]],_Show]

Special cases

With[{class="Pasechnik"},TextGrid[Sort[{Lookup[GraphData[#,"NotationRules"],class],GraphData[#,"V"],#}&/@GraphData[class]],Dividers->All,Alignment->{{Left,Decimal,Left}}]]

Properties

VertexCount

Function[{gn,n},{gn,GraphData[gn,"V"],(4n-1)^2}]@@@({#,Sequence@@Lookup[GraphData[#,"NotationRules"],"Pasechnik"]}&/@GraphData["Pasechnik"])

DeleteCases[%,{_,x_,x_}]

Construction

https://doc.sagemath.org/html/en/reference/graphs/sage/graphs/graph_generators.html#sage.graphs.graph_generators.GraphGenerators.PasechnikGraph

Table[(4n-1)^2,{n,7}]

ps=Table[SageGraph[SageEvaluate["graphs.PasechnikGraph("<>ToString[n]<>").edges()"]],{n,6}]

VertexCount/@ps

RecognizeGraph/@ps

RegularParameters/@ps//Column

TextGrid[Table[{(4n-1)^2,2(((2n-1))^2),4n^2-6n+3,2n(2n+1)},{n,5}],Dividers->All,Alignment->Decimal]

GraphData

GraphDataClassString

GraphDataClassString[g]

GraphDataString

file=OpenAppend["~/new.m"]

Do[WriteString[file,GraphDataString[g[i],
"StandardName"->{"Pasechnik",i},
"Name"->ToString[i]<>"\[Hyphen]Pasechnik graph",
"Information"->None,
"NotationRules"->{"Pasechnik"->i},
"Classes"->{"Pasechnik"},
"Embeddings"->{},
"Skip"->{"Arboricity","BurningNumber","Chord","ChordlessCycle","ChordlessCycles","Chords","ChromaticNumber","CliqueCoveringNumber","ComplementOddChordlessCycle","ComplementOddChordlessCycles","ConnectedInducedSubgraphPolynomial","ConnectedInducedSubgraphs","CrossingNumber","Cycles","CyclePolynomial","DominatingSet","DominatingSets","EdgeCovers","GracefulLabeling","GracefulLabelings","HamiltonianCycles","HamiltonianPaths","HamiltonianWalks","IdiosyncraticPolynomial","IndependentVertexSets","LongestCycles","MatchingGeneratingPolynomial","MaximalIndependentEdgeSets","MaximalIndependentVertexSets","MaximallyNonhamiltonian","MaximumFlowMatrix","MaximumIndependentEdgeSets","MinimumCoveringsByMaximalCliques","MinimumEdgeColoring","MinimumVertexColoring","MinimumVertexCut","MinimumVertexCuts","MinimumWeightFractionalColoring","MinimumWeightFractionalEdgeColoring","OddChordlessCycles","PathPolynomial","Paths","RadioLabeling","RadioLabelings","RadioNumber","RectilinearCrossingCount","ResistanceMatrix","Skewness","StronglyPerfect","UnitDistance","VertexCover","Thickness"},
TimeConstraint->10
]],{i,2,5}]

Close[file]