64 relations: Balinski's theorem, Bijection, Binary number, Bipartite graph, Boolean algebra (structure), Carla Savage, Cartesian product of graphs, Chessboard, Complete coloring, Complete graph, Cube, Cube-connected cycles, Cubic graph, Cycle (graph theory), De Bruijn graph, Disjoint union, Distance-regular graph, Edge (geometry), Expander graph, Fibonacci cube, Folded cube graph, Frankl–Rödl graph, Graph bandwidth, Graph coloring, Graph drawing, Graph theory, Gray code, Halved cube graph, Hamiltonian path, Hamming distance, Hamming graph, Hasse diagram, Hypercube, Induced subgraph, Journal of Combinatorial Theory, K-vertex-connected graph, Knight's graph, Lévy family of graphs, Levi graph, Longest path problem, Matching (graph theory), Mathematical induction, Möbius configuration, Median graph, N-skeleton, Network topology, Pancyclic graph, Partial cube, Path (graph theory), Permutation, ..., Planar graph, Regular graph, Set (mathematics), Snake-in-the-box, Spanning tree, Subset, Symmetric graph, Szymanski's conjecture, Torus, Unit distance graph, Unit vector, Vertex (geometry), Vertex (graph theory), Wreath product. Expand index (14 more) » « Shrink index
In polyhedral combinatorics, a branch of mathematics, Balinski's theorem is a statement about the graph-theoretic structure of three-dimensional polyhedra and higher-dimensional polytopes.
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph.
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice.
Carla Diane Savage is an American computer scientist and mathematician, a professor of computer science at North Carolina State University and the secretary of the American Mathematical Society.
In graph theory, the Cartesian product G \square H of graphs G and H is a graph such that.
A chessboard is the type of checkerboard used in the board game chess, consisting of 64 squares (eight rows and eight columns).
In graph theory, complete coloring is the opposite of harmonious coloring in the sense that it is a vertex coloring in which every pair of colors appears on at least one pair of adjacent vertices.
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
In graph theory, the cube-connected cycles is an undirected cubic graph, formed by replacing each vertex of a hypercube graph by a cycle.
In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three.
In graph theory, a cycle is a path of edges and vertices wherein a vertex is reachable from itself.
In graph theory, an n-dimensional De Bruijn graph of m symbols is a directed graph representing overlaps between sequences of symbols.
In set theory, the disjoint union (or discriminated union) of a family of sets is a modified union operation that indexes the elements according to which set they originated in.
In mathematics, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and i.
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.
In combinatorics, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion as described below.
The Fibonacci cubes or Fibonacci networks are a family of undirected graphs with rich recursive properties derived from its origin in number theory.
In graph theory, a folded cube graph is an undirected graph formed from a hypercube graph by adding to it a perfect matching that connects opposite pairs of hypercube vertices.
In graph theory and computational complexity theory, a Frankl–Rödl graph is a graph defined by connecting pairs of vertices of a hypercube that are at a specified even distance from each other.
In graph theory, the graph bandwidth problem is to label the n vertices vi of a graph G with distinct integers f(vi) so that the quantity \max\ is minimized (E is the edge set of G).
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.
Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics.
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
The reflected binary code (RBC), also known just 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).
In graph theory, the halved cube graph or half cube graph of order n is the graph of the demihypercube, formed by connecting pairs of vertices at distance exactly two from each other in the hypercube graph.
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once.
In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different.
Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics and computer science.
In order theory, a Hasse diagram is a type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction.
In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.
In graph theory, an induced subgraph of a graph is another graph, formed from a subset of the vertices of the graph and all of the edges connecting pairs of vertices in that subset.
The Journal of Combinatorial Theory, Series A and Series B, are mathematical journals specializing in combinatorics and related areas.
In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed.
In graph theory, a knight's graph, or a knight's tour graph, is a graph that represents all legal moves of the knight chess piece on a chessboard.
In graph theory, a branch of mathematics, a Lévy family of graphs is a family of graphs Gn, n.
In combinatorial mathematics, a Levi graph or incidence graph is a bipartite graph associated with an incidence structure.
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph.
In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices.
Mathematical induction is a mathematical proof technique.
In geometry, the Möbius configuration or Möbius tetrads is a certain configuration in Euclidean space or projective space, consisting of two mutually inscribed tetrahedra: each vertex of one tetrahedron lies on a face plane of the other tetrahedron and vice versa.
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.
In mathematics, particularly in algebraic topology, the of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the.
Network topology is the arrangement of the elements (links, nodes, etc.) of a communication network.
In the mathematical study of graph theory, a pancyclic graph is a directed graph or undirected graph that contains cycles of all possible lengths from three up to the number of vertices in the graph.
In graph theory, a partial cube is a graph that is an isometric subgraph of a hypercube.
In graph theory, a path in a graph is a finite or infinite sequence of edges which connect a sequence of vertices which, by most definitions, are all distinct from one another.
In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency.
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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.
In the mathematical field of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G, with minimum possible number of edges.
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1—v1 and u2—v2 of G, there is an automorphism such that In other words, a graph is symmetric if its automorphism group acts transitively upon ordered pairs of adjacent vertices (that is, upon edges considered as having a direction).
In mathematics, Szymanski's conjecture, named after, states that every permutation on the n-dimensional doubly directed hypercube graph can be routed with edge-disjoint paths.
In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.
In mathematics, and particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting two points by an edge whenever the distance between the two points is exactly one.
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
In mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).
In mathematics, the wreath product of group theory is a specialized product of two groups, based on a semidirect product.