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The star graph S_n of order n, sometimes simply known as an "n-star" (Harary 1994, pp. 17-18; Pemmaraju and Skiena 2003, p. 248; Tutte 2005, p. 23), is a tree on n nodes with ...

A complete oriented graph (Skiena 1990, p. 175), i.e., a graph in which every pair of nodes is connected by a single uniquely directed edge. The first and second 3-node ...

A graceful labeling (or graceful numbering) is a special graph labeling of a graph on m edges in which the nodes are labeled with a subset of distinct nonnegative integers ...

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...

A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node ...

A fixed point for which the stability matrix has eigenvalues of the form lambda_+/-=-alpha+/-ibeta (with alpha,beta>0).

A fixed point for which the stability matrix has one zero eigenvector with negative eigenvalue lambda<0.

A fixed point for which the stability matrix has eigenvalues of the form lambda_+/-=alpha+/-ibeta (with alpha,beta>0).

A fixed point for which the stability matrix has one zero eigenvector with positive eigenvalue lambda>0.

Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...