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A Markov chain is collection of random variables {X_t} (where the index t runs through 0, 1, ...) having the property that, given the present, the future is conditionally ...

A circulant graph is a graph of n graph vertices in which the ith graph vertex is adjacent to the (i+j)th and (i-j)th graph vertices for each j in a list l. The circulant ...

The m×n queen graph Q_(m,n) is a graph with mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a queen. ...

The phrase dependent percolation is used in two-dimensional discrete percolation to describe any general model in which the states of the various graph edges (in the case of ...

A planar straight line embedding of a planar graph is a planar embedding in which only straight line segments are used to connect the graph vertices. Fáry (1948) showed that ...

A Turán graph, sometimes called a maximally saturated graph (Zykov 1952, Chao and Novacky 1982), with positive integer parameters n and k is a type of extremal graph on n ...

A biconnected graph is a connected graph having no articulation vertices (Skiena 1990, p. 175). An equivalent definition for graphs on more than two vertices is a graph G ...

A distance-heredity graph, also known as a completely separable graph, is a graph G such that the distance matrix of every connected vertex-induced subgraph G_V of G is the ...

Vince and Bóna (2012) define an assembly tree T for a connected simple graph G on n nodes as a binary rooted tree with n leavesTree Leaf and n-1 internal nodes and satisfying ...

An automorphic graph is a distance-transitive graph Gamma for which the automorphism group Aut(Gamma) acts primitively on the vertices of Gamma and is not a complete graph or ...