EdgeChromaticNumber[g] gives the fewest number of colors necessary to color each edge of graph g, so that no two edges incident on the same vertex have the same color.

EdgeColoring[g] uses Brelaz's heuristic to find a good, but not necessarily minimal, edge coloring of graph g.

EdgeColor is an option that allows the user to associate colors with edges. Black is the default color. EdgeColor can be set as part of the graph data structure or in ...

EdgeDirection is an option that takes on values True or False allowing the user to specify whether the graph is directed or not. EdgeDirection can be set as part of the graph ...

EdgeWeight is an option that allows the user to associate weights with edges. 1 is the default weight. EdgeWeight can be set as part of the graph data structure.

FranklinGraph returns a 12-vertex graph that represents a 6-chromatic map on the Klein bottle. It is the sole counterexample to Heawood's map-coloring conjecture.

GraphJoin[g_1, g_2, ...] constructs the join of graphs g_1, g_2, and so on. This is the graph obtained by adding all possible edges between different graphs to the graph ...

GraphPower[g, k] gives the k\[Null]^th power of graph g. This is the graph whose vertex set is identical to the vertex set of g and that contains an edge between vertices i ...

MeredithGraph returns a 4-regular, 4-connected graph that is not Hamiltonian, providing a counterexample to a conjecture by C. St. J. A. Nash\[Dash]Williams.

MinimumSpanningTree[g] uses Kruskal's algorithm to find a minimum spanning tree of graph g.