the mathematical field of graph theory, a permutation graph is a graph whose vertices represent the elements of a permutation, and whose edges represent...

being incomparability graphs, permutation graphs are comparability graphs. In fact, the permutation graphs are exactly the graphs that are both comparability...

of graphs as well. For instance, in a circle graph, the neighborhood of each vertex is a permutation graph, so a maximum clique in a circle graph can...

In graph theory, a uniquely colorable graph is a k-chromatic graph that has only one possible (proper) k-coloring up to permutation of the colors. Equivalently...

Planar graphs (In fact, planar graph isomorphism is in log space, a class contained in P) Interval graphs Permutation graphs Circulant graphs Bounded-parameter...

layers: Permutation equivariant: a permutation equivariant layer maps a representation of a graph into an updated representation of the same graph. In the...

the forbidden permutation patterns 2413 and 3142; they are also the permutations whose permutation graphs are cographs and the permutations that realize...

interval graphs, and more generally to graphs of bounded tree-length, such as chordal graphs, permutation graphs or asteroidal-triple-free graphs. Deciding...

unconstrained permutations. Every permutation defines a permutation graph, a graph whose vertices are the elements of the permutation and whose edges...

largest clique in a permutation graph corresponds to the longest decreasing subsequence of the permutation that defines the graph (assuming the original...

Permutation graph Permutation pattern Permutation polynomial Permutohedron Rencontres numbers Robinson–Schensted correspondence Sum of permutations:...

that are out of their natural order. Let π {\displaystyle \pi } be a permutation. There is an inversion of π {\displaystyle \pi } between i {\displaystyle...

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed...

edge–vertex connectivity. Formally, an automorphism of a graph G = (V, E) is a permutation σ of the vertex set V, such that the pair of vertices (u,...

comparability graph, it follows that graph and its complement are both interval graphs if and only if the graph is both a split graph and a permutation graph. The...

entries 0.: 26  An n × n permutation matrix can represent a permutation of n elements. Pre-multiplying an n-row matrix M by a permutation matrix P, forming PM...

circle graphs as a special case. Every distance-hereditary graph is a circle graph, as is every permutation graph and every indifference graph. Every...

notion of permutation graph, in turn they are a special case of the family of the complements of comparability graphs known as cocomparability graphs. A unit...

dihedral permutation of its outer cycle. Chartrand and Harary also proved an analogue of Kuratowski's theorem for outerplanar graphs, that a graph is outerplanar...

special cases of the distance-hereditary graphs, permutation graphs, comparability graphs, and perfect graphs. Any cograph may be constructed using the...

of graph theory, an automorphism is a permutation of the vertices such that edges are mapped to edges and non-edges are mapped to non-edges. A graph is...

in polynomial time whether the subchromatic number of interval and permutation graphs is at most r (Broersma et al. 2002). Albertson, M. O.; Jamison, R...

Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...

In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain...

is a permutation of the elements of a set in which no element appears in its original position. In other words, a derangement is a permutation that has...

weighted trees, on block graphs, on cacti, on bipartite permutation graphs, and on Ptolemaic graphs. For the class of interval graphs, an O ( n 4 ) {\displaystyle...

groups of graphs, such as the Higman–Sims group and the Higman–Sims graph. The elements of the symmetric group on a set X are the permutations of X. The...

In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract...

In mathematics, a permutation of a set can mean one of two different things: an arrangement of its members in a sequence or linear order, or the act or...

vertices of the graph are considered to be labeled in such a way as to be distinguishable from each other, while in other problems any permutation of the vertices...