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A spider graph, spider tree, or simply "spider," is a tree with one vertex of degree at least 3 and all others with degree at most 2. The numbers of spiders on n=1, 2, ... ...

A matchstick graph is a simple graph which has a graph embedding that is planar, for which all distances between vertices have unit distance, and which is non-degenerate (so ...

The triangular grid graph T_n is the lattice graph obtained by interpreting the order-(n+1) triangular grid as a graph, with the intersection of grid lines being the vertices ...

The Moscow-Soicher graph is a weakly regular graph on 672 vertices with parameters (nu,k,lambda,mu)=(672,110,28,(0,18)). It is distance-regular but not distance-transitive ...

The Ionin-Kharaghani graph is a strongly regular graph on 765 vertices and 73440 edges. It has regular parameters (nu,k,lambda,mu)=(765,192,48,48). It is implemented in the ...

The truncated pentakis dodecahedral graph, illustrated above in a pair of embeddings, is the skeleton of the truncated pentakis dodecahedron. It has 180 vertices, 270 edges, ...

A uniquely pancyclic graph is a graph that has exactly one cycle of each length between 3 and the graph's vertex count. Uniquely pancyclic graphs are therefore a special case ...

The term "Euler graph" is sometimes used to denote a graph for which all vertices are of even degree (e.g., Seshu and Reed 1961). Note that this definition is different from ...

A noneulerian graph is a graph that is not Eulerian. The numbers of simple noneulerian graphs on n=1, 2, ... nodes are 2, 3, 10, 30, 148, 1007, 12162, 272886, ... (OEIS ...

The Goddard-Henning graph, illustrated above in several embeddings, is the 9-node planar graph of graph diameter 2 having domination number gamma=3. It was first constructed ...