Elementary Invariants of a Graph

Order(G): Grph -> RngIntElt

NumberOfVertices(G): Grph -> RngIntElt

The number of vertices of the graph \(G\).

Size(G): Grph -> RngIntElt

NumberOfEdges(G): Grph -> RngIntElt

The number of edges of the graph \(G\).

CharacteristicPolynomial(G): GrphUnd -> RngUPolElt

The characteristic polynomial (over the integers) of the graph \(G\); i.e. the characteristic polynomial of the adjacency matrix of \(G\).

Spectrum(G): GrphUnd -> SetEnum

The spectrum of the graph \(G\); i.e. the roots of the characteristic polynomial of \(G\). The roots are returned as a set of tuples, each containing a root and its multiplicity.