LabeledGraph

A name from the enumeratio catalogue with no kernel of its own yet; this page carries its crosswalk only.

As a single-graded labeled_graph

LabeledGraph(...)As a single-graded labeled_graph

Typed signatures

Type	Package	Applies
(tuple<integer, list<list<integer>>>) -> labeled_graph	combinatorics	always

Domain: Combinatorics

Statistics

On LabeledGraph, called as CombinatorialStat(x, "Name").

• AlbertsonIndexSt001351The sum over the edges of the difference of the degrees of its ends.
• BridgeCountSt001479The edges whose deletion leaves more components.
• ChromaticNumberSt000098The fewest colors for the vertices so that adjacent vertices differ.
• CliqueNumberSt000097The most vertices that are pairwise adjacent.
• ComplementComponentCountSt000286The connected components of the complement graph.
• ConnectedInducedSubgraphCountSt001441The nonempty sets of vertices that induce a connected subgraph.
• CutVertexCountSt000552The vertices whose deletion leaves more components.
• CyclomaticNumberSt001311The edges less the vertices plus the components: the independent cycles.
• DegreeTwoVertexCountSt000313The vertices with exactly two edges.
• DistanceFourPairCountSt000449The pairs of vertices at distance 4.
• DistanceThreePairCountSt000447The pairs of vertices at distance 3.
• DistanceTwoPairCountSt000448The pairs of vertices at distance 2.
• EvenDegreeVertexCountSt000309The vertices with an even number of edges.
• FirstZagrebIndexSt000465The sum of the squares of the degrees.
• ForgottenIndexSt000571The sum of the cubes of the degrees.
• FourCliqueCountSt001309The sets of four vertices that are pairwise adjacent.
• GraphComponentCountSt000287The connected components: the vertices that are the first of their component.
• GraphEdgeCountSt000081The edges of the graph.
• GraphLeafCountSt000312The vertices with exactly one edge.
• HosoyaIndexSt000468The sets of edges with no two sharing a vertex, the empty set included.
• IndependenceNumberSt000093The most vertices that are pairwise non-adjacent.
• IndependentSetCountSt000300The sets of vertices, the empty set included, with no two adjacent.
• InducedPathOnThreeVerticesCountSt001308The sets of three vertices that induce a path: exactly two of the three edges.
• IsolatedVertexCountSt000315The vertices with no edge.
• MatchingNumberSt000387The most edges with no two sharing a vertex.
• MaximalIndependentSetCountSt001304The independent sets of vertices that no vertex can be added to.
• MaximumDegreeSt000171The greatest number of edges at one vertex.
• MaximumDegreeVertexCountSt001368The vertices whose degree is the greatest.
• MaximumDistanceSt000259The greatest distance between two vertices: the diameter.
• MinimumDegreeSt000310The fewest edges at one vertex.
• MinimumEccentricitySt000260The least eccentricity of a vertex, the greatest distance from it to another vertex: the radius.
• OddDegreeVertexCountSt000311The vertices with an odd number of edges.
• OreDegreeSt000915The greatest sum of the degrees of the two ends of an edge.
• SecondZagrebIndexSt000361The sum over the edges of the product of the degrees of its ends.
• TotalIrregularitySt001522The sum over the unordered pairs of vertices of the difference of their degrees.
• TriangleCountSt000095The triples of vertices that are pairwise adjacent.
• TriangleVertexCountSt001995The vertices on a triangle.
• VertexCoverNumberSt000362The fewest vertices that meet every edge: the vertices less the independence number.
• WienerIndexSt000265The sum of the distances over the pairs of vertices that are joined by a path.

Maps

Into and out of LabeledGraph, called as CombinatorialMap(x, "Name"). Properties are the laws we state and what FindStat records.

28 more in FindStat, not implemented here

• Mp00011BinaryTree → LabeledGraphGraded mapto graph
• Mp00037LabeledGraph → IntegerPartitionSurjectionGraded mapto partition of connected components
• Mp00046OrderedTree → LabeledGraphGraded mapto graph
• Mp00074Posets → LabeledGraphGraded mapto graph
• Mp00111LabeledGraph → LabeledGraphBijectionGraded mapInvolutioncomplement
• Mp00117LabeledGraph → LabeledGraphIdempotentGraded mapOre closure
• Mp00147LabeledGraph → LabeledGraphGraded mapsquare
• Mp00152LabeledGraph → IntegerCompositionSurjectionGraded mapLaplacian multiplicities
• Mp00154LabeledGraph → LabeledGraphIdempotentcore
• Mp00156LabeledGraph → LabeledGraphline graph
• Mp00157LabeledGraph → LabeledGraphGraded mapInvolutionconnected complement
• Mp00160Permutation → LabeledGraphGraded mapgraph of inversions
• Mp00184IntegerComposition → LabeledGraphInjectionGraded mapto threshold graph
• Mp00198Posets → LabeledGraphGraded mapincomparability graph
• Mp00203LabeledGraph → LabeledGraphInjectionGraded mapcone
• Mp00243LabeledGraph → Posetsweak duplicate order
• Mp00247LabeledGraph → LabeledGraphIdempotentde-duplicate
• Mp00250LabeledGraph → LabeledGraphclique graph
• Mp00251LabeledGraph → IntegerPartitionclique sizes
• Mp00259LabeledGraph → LabeledGraphInjectionGraded mapvertex addition
• Mp00264LabeledGraph → LabeledGraphIdempotentdelete endpoints
• Mp00266LabeledGraph → Latticesconnected vertex partitions
• Mp00274LabeledGraph → LabeledGraphblock-cut tree
• Mp00275LabeledGraph → IntegerPartitionSurjectionto edge-partition of connected components
• Mp00276LabeledGraph → IntegerPartitionto edge-partition of biconnected components
• Mp00318LabeledGraph → LabeledGraphInvolutiondual on components
• Mp00324LabeledGraph → IntegerCompositionGraded mapchromatic difference sequence
• Mp00335Lattices → LabeledGraphzero-divisor graph

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