Concept
Hypercube graph
Related concepts (16)
Median graph
In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a, b, and c have a unique median: a vertex m(a,b,c) that belongs to shortest paths between each pair of a, b, and c. The concept of median graphs has long been studied, for instance by or (more explicitly) by , but the first paper to call them "median graphs" appears to be . As Chung, Graham, and Saks write, "median graphs arise naturally in the study of ordered sets and discrete distributive lattices, and have an extensive literature".
Snake-in-the-box
The snake-in-the-box problem in graph theory and computer science deals with finding a certain kind of path along the edges of a hypercube. This path starts at one corner and travels along the edges to as many corners as it can reach. After it gets to a new corner, the previous corner and all of its neighbors must be marked as unusable. The path should never travel to a corner which has been marked unusable.
Partial cube
In graph theory, a partial cube is a graph that is isometric to a subgraph of a hypercube. In other words, a partial cube can be identified with a subgraph of a hypercube in such a way that the distance between any two vertices in the partial cube is the same as the distance between those vertices in the hypercube. Equivalently, a partial cube is a graph whose vertices can be labeled with bit strings of equal length in such a way that the distance between two vertices in the graph is equal to the Hamming distance between their labels.
Distance-transitive graph
In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y. Distance-transitive graphs were first defined in 1971 by Norman L. Biggs and D. H. Smith. A distance-transitive graph is interesting partly because it has a large automorphism group.
Gray code
The reflected binary code (RBC), also known as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit). For example, the representation of the decimal value "1" in binary would normally be "" and "2" would be "". In Gray code, these values are represented as "" and "". That way, incrementing a value from 1 to 2 requires only one bit to change, instead of two.
Edge (geometry)
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon, an edge is a line segment on the boundary, and is often called a polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides) meet. A segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal.
Graph power
In graph theory, a branch of mathematics, the kth power G^k of an undirected graph G is another graph that has the same set of vertices, but in which two vertices are adjacent when their distance in G is at most k. Powers of graphs are referred to using terminology similar to that of exponentiation of numbers: G^2 is called the square of G, G^3 is called the cube of G, etc. Graph powers should be distinguished from the products of a graph with itself, which (unlike powers) generally have many more vertices than the original graph.
Induced path
In the mathematical area of graph theory, an induced path in an undirected graph G is a path that is an induced subgraph of G. That is, it is a sequence of vertices in G such that each two adjacent vertices in the sequence are connected by an edge in G, and each two nonadjacent vertices in the sequence are not connected by any edge in G. An induced path is sometimes called a snake, and the problem of finding long induced paths in hypercube graphs is known as the snake-in-the-box problem.
Hamming graph
Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics (graph theory) and computer science. Let S be a set of q elements and d a positive integer. The Hamming graph H(d,q) has vertex set S^d, the set of ordered d-tuples of elements of S, or sequences of length d from S. Two vertices are adjacent if they differ in precisely one coordinate; that is, if their Hamming distance is one. The Hamming graph H(d,q) is, equivalently, the Cartesian product of d complete graphs K_q.
Cartesian product of graphs
In graph theory, the Cartesian product G □ H of graphs G and H is a graph such that: the vertex set of G □ H is the Cartesian product V(G) × V(H); and two vertices (u,u' ) and (v,v' ) are adjacent in G □ H if and only if either u = v and u' is adjacent to v' in H, or u' = v' and u is adjacent to v in G. The Cartesian product of graphs is sometimes called the box product of graphs [Harary 1969]. The operation is associative, as the graphs (F □ G) □ H and F □ (G □ H) are naturally isomorphic.