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In a graph G, contraction of an edge e with endpoints u,v is the replacement of u and v with a single vertex such that edges incident to the new vertex are the edges other ...

A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...

A planar embedding, also called a "plane graph" (Harary 1994, p. 103; Harborth and Möller 1994), "planar drawing," or "plane drawing," of a planar graph is an embedding in ...

A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...

Dijkstra's algorithm is an algorithm for finding a graph geodesic, i.e., the shortest path between two graph vertices in a graph. It functions by constructing a shortest-path ...

A maximal clique is a clique that cannot be extended by including one more adjacent vertex, meaning it is not a subset of a larger clique. A maximum clique (i.e., clique of ...

An error-correcting code is an algorithm for expressing a sequence of numbers such that any errors which are introduced can be detected and corrected (within certain ...

The graph corresponding to the complete k-ary tree on n nodes is implemented in the Wolfram Language as KaryTree[n, k].

The Weisfeiler-Leman dimension dim_(WL)(G) of a graph G, sometimes known as the WL dimension, is the smallest integer d such that the d-dimensional Weisfeiler-Leman algorithm ...

The average disorder number of a simple connected graph on n vertices is defined as the average length of a walk along the edges of the graph taken over all ordering of its ...