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The triakis tetrahedral graph is Archimedean dual graph which is the skeleton of the triakis tetrahedron. It is implemented in the Wolfram Language as ...

The Frucht graph is smallest cubic identity graph (Skiena 1990, p. 185). It is implemented in the Wolfram Language as GraphData["FruchtGraph"]. It has 12 vertices and 18 ...

A heptahedral graph is a polyhedral graph on seven nodes. There are 34 nonisomorphic heptahedral graphs, as first enumerated by Kirkman (1862-1863) and Hermes (1899ab, 1900, ...

A graphical partitioning based on the eigenvalues and eigenvectors of the Laplacian matrix of a graph.

The Cameron graph is a strongly regular Hamiltonian graph on 231 vertices with parameters (nu,k,lambda,mu)=(231,30,9,3). It is distance-regular with intersection array ...

A weighted graph in which the weights are equal to the Euclidean lengths of the edges in a specified embedding (Skiena 1990, pp. 201 and 252).

The co-rank of a graph G is defined as s(G)=m-n+c, where m is the number of edges of G, n is the number of vertices, and c is the number of connected components (Biggs 1993, ...

The rank of a graph G is defined as r(G)=n-c, where n is the number of vertices on G and c is the number of connected components (Biggs 1993, p. 25).

A distance-heredity graph, also known as a completely separable graph, is a graph G such that the distance matrix of every connected vertex-induced subgraph G_V of G is the ...

The disdyakis dodecahedral graph is Archimedean dual graph which is the skeleton of the disdyakis dodecahedron. It is implemented in the Wolfram Language as ...