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A directed graph is called an arborescence if, from a given node x known as the root vertex, there is exactly one elementary path from x to every other node y.

The cotree T^* of a spanning tree T in a connected graph G is the spacing subgraph of G containing exactly those edges of G which are not in T (Harary 1994, p. 39).

The maximum degree, sometimes simply called the maximum degree, of a graph G is the largest vertex degree of G, denoted Delta.

The mean clustering coefficient of a graph G is the average of the local clustering coefficients of G. It is implemented in the Wolfram Language as ...

Let a cotree of a spanning tree T in a connected graph G be denoted T^*. Then the edges of G which are not in T^* are called its twigs (Harary 1994, p. 39).

The correspondence which relates the Hanoi graph to the isomorphic graph of the odd binomial coefficients in Pascal's triangle, where the adjacencies are determined by ...

A variation of chess involving a change in the form of the board, the rules of play, or the pieces used. For example, the normal rules of chess can be used but with a ...

The term "lobster" is used to refer either to a particular polyiamond or to a class of tree called a lobster graph. When referring to polyiamonds, the lobster is the ...

The Randić matrix A_(Randic) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=1/(sqrt(d_id_j)), (1) where d_i are the vertex degrees of the graph. In ...

There are (at least) two graphs associated with Horton, illustrated above. The first is a graph on 96 nodes providing a counterexample to the Tutte conjecture that every ...