True if the vertices u and v, both belonging to the same graph G, are adjacent, otherwise false.

e adj f : GrphEdge, GrphEdge -> BoolElt

True if the edges e and f, both belonging to the same graph G, share a common vertex, otherwise false.

True if the vertices u and v, both belonging to the same graph G, are not adjacent, otherwise false.

e notadj f : GrphEdge, GrphEdge -> BoolElt

True if the edges e and f, both belonging to the same graph G, do not share a common vertex, otherwise false.

True if the vertex u is an endpoint of the edge e, where u and e belong to the same graph, otherwise false.

True if the vertex u is not an endpoint of the edge e, where u and e belong to the same graph, otherwise false.

G eq H : GrphUnd, GrphUnd -> BoolElt

True if the graphs G and H are identical, otherwise false.

True if the graph G is a bipartite graph, otherwise false.

True if the graph G, on p vertices, is the complete graph on p vertices, otherwise false.

True if the graph G is a connected graph, otherwise false.

True if the graph G is an eulerian graph, otherwise false.

True if the graph G is a forest, i.e. does not possess any cycles, otherwise false.

True if the graph G is a null graph, otherwise false.

True if the graph G is a path graph, otherwise false.

True if the graph G is a polygon graph, otherwise false.

True if the graph G is a planar graph, otherwise false.

True if the graph G is a regular graph, otherwise false.

True if the graph G is separable, i.e. if G has at least one cut-vertex, otherwise false.

True if the graph G is a tree, otherwise false.