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An alkane graph is a tree in which vertices correspond to atoms and edges to carbon-carbon or hydrogen-carbon bonds in a chemical alkane. In chemistry, an alkane is an ...

The (n,k)-arrangement graph A_(n,k) is defined as the graph on the vertex set consisting of the permutations of {1,2,...,n} containing at most k elements where vertices are ...

The Fritsch graph is the 9-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 comparability graph of a partially ordered set P=(X,<=) is the graph with vertex set X for which vertices x and y are adjacent iff either x<=y or y<=x in P.

A graph G is said to be separable if it is either disconnected or can be disconnected by removing one vertex, called articulation. A graph that is not separable is said to be ...

The n-Andrásfai graph is a circulant graph on 3n-1 nodes whose indices are given by the integers 1, ..., 3n-1 that are congruent to 1 (mod 3). The Andrásfai graphs have graph ...

A shortest path between two graph vertices (u,v) of a graph (Skiena 1990, p. 225). There may be more than one different shortest paths, all of the same length. Graph ...

A chordless graph is a simple graph possessing no chords. A chordal graph (which possesses no chordless cycles) is not the same as (or converse of) a chordless graph (which ...

The assignment of labels or colors to the edges or vertices of a graph. The most common types of graph colorings are edge coloring and vertex coloring.

An integral graph, not to be confused with an integral embedding of a graph, is defined as a graph whose graph spectrum consists entirely of integers. The notion was first ...