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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 Meringer graph is one of the four (5,5)-cage graphs, discovered by Meringer (1999) after it had long been thought that only three such cages existed. Like the other ...

The skeleton of the tesseract, commonly denoted Q_4, is a quartic symmetric graph with girth 4 and diameter 4. The automorphism group of the tesseract is of order 2^7·3=384 ...

A generalized Moore graph is a regular graph of degree r where the counts of vertices at each distance d=0, 1, ... from any vertex are 1, r, r(r-1), r(r-1)^2, r(r-1)^3, ..., ...

A finite simple connected graph G is quadratically embeddable if its quadratic embedding constant QEC(G) is nonpositive, i.e., QEC(G)<=0. A graph being quadratically ...

A Berge graph is a simple graph that contains no odd graph hole and no odd graph antihole. The strong perfect graph theorem asserts that a graph is perfect iff it is a Berge ...

A notion introduced by R. M. Wilson in 1974. Given a finite graph G with n vertices, puz(G) is defined as the graph whose nodes are the labelings of G leaving one node ...

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...

The Reye graph is the transposition graph G_4 of order 4.

A reflexive graph is a pseudograph such that each vertex has an associated graph loop.