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A graph H is a minor of a graph G if a copy of H can be obtained from G via repeated edge deletion and/or edge contraction. The Kuratowski reduction theorem states that any ...

The distance d(u,v) between two vertices u and v of a finite graph is the minimum length of the paths connecting them (i.e., the length of a graph geodesic). If no such path ...

A functional graph is a directed graph in which each vertex has outdegree one, and can therefore be specified by a function mapping {1,...,n} onto itself. Functional graphs ...

The Errera graph is the 17-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

The dodecahedral graph is the Platonic graph corresponding to the connectivity of the vertices of a dodecahedron, illustrated above in four embeddings. The left embedding ...

Every planar graph (i.e., graph with graph genus 0) has an embedding on a torus. In contrast, toroidal graphs are embeddable on the torus, but not in the plane, i.e., they ...

The n-sunlet graph is the graph on 2n vertices obtained by attaching n pendant edges to a cycle graph C_n (ISGCI), i.e., the coronas C_n circledot K_1 (Frucht 1979). Sunlet ...

An arc-transitive graph, sometimes also called a flag-transitive graph, is a graph whose graph automorphism group acts transitively on its graph arcs (Godsil and Royle 2001, ...

An antiprism graph is a graph corresponding to the skeleton of an antiprism. Antiprism graphs are therefore polyhedral and planar. The n-antiprism graph has 2n vertices and ...

There appears to be no term in standard use for a graph with graph crossing number 1. Furthermore, the terms "almost planar" and "1-planar" are used in the literature for ...