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Permutation graph

Index Permutation graph

In mathematics, a permutation graph is a graph whose vertices represent the elements of a permutation, and whose edges represent pairs of elements that are reversed by the permutation. [1]

29 relations: American Journal of Mathematics, Bipartite graph, Circle graph, Clique (graph theory), Clique problem, Cograph, Comparability graph, Complement graph, Discrete Mathematics (journal), Graph theory, Independent set (graph theory), Intersection graph, Inversion (discrete mathematics), Line segment, Longest increasing subsequence, Mathematics, Modular decomposition, NP-completeness, Order dimension, Parallel (geometry), Partially ordered set, Pathwidth, Perfect graph, Permutation, SIAM Journal on Discrete Mathematics, Time complexity, Trapezoid graph, Treewidth, Vertex (graph theory).

American Journal of Mathematics

The American Journal of Mathematics is a bimonthly mathematics journal published by the Johns Hopkins University Press.

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Bipartite graph

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.

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Circle graph

In graph theory, a circle graph is the intersection graph of a set of chords of a circle.

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Clique (graph theory)

In the mathematical area of graph theory, a clique is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent; that is, its induced subgraph is complete.

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Clique problem

In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph.

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Cograph

In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation and disjoint union.

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Comparability graph

In graph theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a partial order.

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Complement graph

In graph theory, the complement or inverse of a graph is a graph on the same vertices such that two distinct vertices of are adjacent if and only if they are not adjacent in.

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Discrete Mathematics (journal)

Discrete Mathematics is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications.

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Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

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Independent set (graph theory)

In graph theory, an independent set or stable set is a set of vertices in a graph, no two of which are adjacent.

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Intersection graph

In the mathematical area of graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets.

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Inversion (discrete mathematics)

In computer science and discrete mathematics a sequence has an inversion where two of its elements are out of their natural order.

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Line segment

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.

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Longest increasing subsequence

In computer science, the longest increasing subsequence problem is to find a subsequence of a given sequence in which the subsequence's elements are in sorted order, lowest to highest, and in which the subsequence is as long as possible.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Modular decomposition

In graph theory, the modular decomposition is a decomposition of a graph into subsets of vertices called modules. A module is a generalization of a connected component of a graph.

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NP-completeness

In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.

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Order dimension

In mathematics, the dimension of a partially ordered set (poset) is the smallest number of total orders the intersection of which gives rise to the partial order.

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Parallel (geometry)

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.

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Partially ordered set

In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

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Pathwidth

In graph theory, a path decomposition of a graph G is, informally, a representation of G as a "thickened" path graph, and the pathwidth of G is a number that measures how much the path was thickened to form G.

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Perfect graph

In graph theory, a perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph.

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Permutation

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.

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SIAM Journal on Discrete Mathematics

SIAM Journal on Discrete Mathematics is a peer-reviewed mathematics journal published quarterly by the Society for Industrial and Applied Mathematics (SIAM).

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Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.

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Trapezoid graph

In graph theory, trapezoid graphs are intersection graphs of trapezoids between two horizontal lines.

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Treewidth

In graph theory, the treewidth of an undirected graph is a number associated with the graph.

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Vertex (graph theory)

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).

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References

[1] https://en.wikipedia.org/wiki/Permutation_graph

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