ConnectedQ[g] yields True if undirected graph g is connected. If g is directed, the function returns True if the underlying undirected graph is connected. ConnectedQ[g, ...

DeleteEdge[g, e] gives graph g minus e. If g is undirected, then e is treated as an undirected edge; otherwise it is treated as a directed edge. If there are multiple edges ...

DeleteEdges[g, edgeList] gives graph g minus the list of edges edgeList. If g is undirected, then the edges in edgeList are treated as undirected edges; otherwise they are ...

Dijkstra[g, v] gives a shortest-path spanning tree and associated distances from vertex v of graph g. The shortest-path spanning tree is given by a list in which element i is ...

DominationLattice[n] returns a Hasse diagram of the partially ordered set on integer partitions of n in which p < q if q dominates p. The function takes two options: Type and ...

Edges[g] gives the list of edges in g. Edges[g, All] gives the edges of g along with the graphics options associated with each edge. Edges[g, EdgeWeight] returns the list of ...

FromAdjacencyLists[l] constructs an edge list representation for a graph from the given adjacency lists l, using a circular embedding. FromAdjacencyLists[l, v] uses v as the ...

FromUnorderedPairs[l] constructs an edge list representation from a list of unordered pairs l, using a circular embedding.FromUnorderedPairs[l, v] uses v as the embedding for ...

GeneralizedPetersenGraph[n, k] returns the generalized Petersen graph, for integers n > 1 and k > 0, which is the graph with vertices {u_1, u_2, ..., u_n} and {v_1, v_2, ..., ...

GraphPolynomial[n, x] returns a polynomial in x in which the coefficient of x^m is the number of nonisomorphic graphs with n vertices and m edges. GraphPolynomial[n, x, ...