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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 pentatope is the simplest regular figure in four dimensions, representing the four-dimensional analog of the solid tetrahedron. It is also called the 5-cell, since it ...

A uniquely k-colorable graph G is a chi-colorable graph such that every chi-coloring gives the same partition of G (Chao 2001). Examples of uniquely minimal colorable classes ...

Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. The number of degree sequences for ...

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 shuffle-exchange graph is a nonsimple graph (due to the existence of graph loops) whose vertices are length n binary strings with an edge from w to w^' if 1. w^' differs ...

The ratio of the independence number of a graph G to its vertex count is known as the independence ratio of G (Bollobás 1981). The product of the chromatic number and ...

The n-Pasechnik graph is a strongly regular graph on (4n-1)^2 vertices constructed from a skew Hadamard matrix of order 4n. It has regular parameters . The 1-Pasechnik is ...

The dimension e(G), also called the Euclidean dimension (e.g., Buckley and Harary 1988) of a graph, is the smallest dimension n of Euclidean n-space in which G can be ...

There are several related theorems involving Hamiltonian cycles of graphs that are associated with Pósa. Let G be a simple graph with n graph vertices. 1. If, for every k in ...