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De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...

The term "God's number" is sometimes given to the graph diameter of Rubik's graph, which is the minimum number of turns required to solve a Rubik's cube from an arbitrary ...

The global clustering coefficient C of a graph G is the ratio of the number of closed trails of length 3 to the number of paths of length two in G. Let A be the adjacency ...

A minimal edge cover is an edge cover of a graph that is not a proper subset of any other edge cover. Every minimum edge cover is a minimal edge cover, but the converse does ...

A weakly connected component of a simple directed graph (i.e., a digraph without loops) is a maximal subdigraph such that for every pair of distinct vertices u, v in the ...

The apeirogon is an extension of the definition of regular polygon to a figure with an infinite number of sides. Its Schläfli symbol is {infty}. The apeirogon can produce a ...

A pseudotree is a connected pseudoforest, i.e., an undirected connected graph that contains at most one graph cycle. Connected acyclic graphs (i.e., trees), are therefore ...

A labeled graph whose nodes are indexed by the generators of a Coxeter group having (P_i,P_j) as an graph edge labeled by M_(ij) whenever M_(ij)>2, where M_(ij) is an element ...

The Danzer configuration is a 35_4 self-dual configuration of 35 lines and 35 points in which 4 points lie on each line and 4 lines pass through each point. The Levi graph of ...

The inequality sinAsinBsinC<=((3sqrt(3))/(2pi))^3ABC, where A, B, and C are the vertex angles of a triangle. The maximum is reached for an equilateral triangle (and therefore ...