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The complete bipartite graph K_(1,3) is a tree known as the "claw." It is isomorphic to the star graph S_4, and is sometimes known as the Y graph (Horton and Bouwer 1991; ...

The antenna graph is the graph on 6 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["AntennaGraph"].

The n-centipede graph, n-centipede tree, n-comb graph (Seoud and Youssef 2017), or simply "n-centipede," is the tree on 2n nodes obtained by joining the bottoms of n copies ...

A polyhedral graph corresponding to the skeleton of a Platonic solid. The five platonic graphs, the tetrahedral graph, cubical graph, octahedral graph, dodecahedral graph, ...

The fish graph is the graph on 6 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["FishGraph"].

Call a graph vertex m(a,b,c) a median of a graph G if it lies on all shortest paths between each pair of vertices (a,b), (b,a), and (c,a) in G. A median graph is then defined ...

The n-cycle complement graph C^__n is the graph complement of the cycle graph C_n. Cycle complement graphs are special cases of circulant graphs. The first few are ...

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 ...