23 relations: Bipartite graph, Cayley graph, Characteristic polynomial, Chirality, Cubic graph, Dihedral group, Distance (graph theory), Distance-transitive graph, Edge coloring, Girth (graph theory), Graph automorphism, Graph coloring, Graph theory, Group action, Hamiltonian path, K-edge-connected graph, K-vertex-connected graph, LCF notation, Marston Conder, Mathematics, Regular map (graph theory), Symmetric graph, Torus.
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 mathematics, a Cayley graph, also known as a Cayley colour graph, Cayley diagram, group diagram, or colour group is a graph that encodes the abstract structure of a group.
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots.
Chirality is a property of asymmetry important in several branches of science.
In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three.
In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.
In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them.
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.
In graph theory, an edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two adjacent edges have the same color.
In graph theory, the girth of a graph is the length of a shortest cycle contained in the graph.
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving the edge–vertex connectivity.
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.
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.
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 graph theory, a connected graph is k-edge-connected if it remains connected whenever fewer than k edges are removed.
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 combinatorial mathematics, LCF notation or LCF code is a notation devised by Joshua Lederberg, and extended by H. S. M. Coxeter and Robert Frucht, for the representation of cubic graphs that contain a Hamiltonian cycle.
Marston Donald Edward Conder (born September 1955) is a New Zealand mathematician, a Distinguished Professor of Mathematics at Auckland University,, Auckland U. Mathematics, retrieved 2013-01-22.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
In mathematics, a regular map is a symmetric tessellation of a closed surface.
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 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.