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 ...

DepthFirstTraversal[g, v] performs a depth-first traversal of graph g starting from vertex v, and gives a list of vertices in the order in which they were encountered. ...

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 ...

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 ...

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, ...

GridGraph[n, m] constructs an n*m grid graph, the product of paths on n and m vertices. GridGraph[p, q, r] constructs a p*q*r grid graph, the product of GridGraph[p, q] and a ...

IncidenceMatrix[g] returns the (0, 1)-matrix of graph g, which has a row for each vertex and a column for each edge and (v, e) = 1 if and only if vertex v is incident upon ...

KSubsetGroup[pg, s] returns the group induced by a permutation group pg on the set s of k-subsets of [n], where n is the index of pg. The optional argument Type can be ...

ListNecklaces[n, c, Cyclic] returns all distinct necklaces whose beads are colored by colors from c. Here c is a list of n, not necessarily distinct colors, and two colored ...

NecklacePolynomial[n, c, Cyclic] returns a polynomial in the colors in c whose coefficients represent numbers of ways of coloring an n-bead necklace with colors chosen from ...