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A graph for which every node has finite degree.

The diamond graph is the simple graph on 4 nodes and 5 edges illustrated above (Brandstädt et al. 1987, p. 18). It is isomorphic to the complete tripartite graph K_(1,1,2) ...

The Soifer graph, illustrated above in a number of embeddings, is a planar graph on 9 nodes that tangles the Kempe chains in Kempe's algorithm and thus provides an example of ...

The equation of a line ax+by+c=0 in slope-intercept form is given by y=-a/bx-c/b, (1) so the line has slope -a/b. Now consider the distance from a point (x_0,y_0) to the ...

An outerplanar graph is a graph that can be embedded in the plane such that all vertices lie on the outer face. Outerplanar graphs are planar and, by their definition, ...

The pentakis icosidodecahedral graph, illustrated above, is a graph on 42 vertices that is the skeleton of the pentakis icosidodecahedron.

The parachute graph is the graph on 7 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["ParachuteGraph"].

The parapluie (French for 'umbrella') graph is the graph on 7 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["ParapluieGraph"].

The Soicher graphs are three distance-regular graphs on 5346, 486, and 315 vertices, respectively. The first two are also distance-transitive but the third is not. The second ...

For a permutation alpha in the symmetric group S_p, the alpha-permutation graph of a labeled graph G is the graph union of two disjoint copies of G (say, G_1 and G_2), ...