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A skew-symmetric graph is a graph that is isomorphic to its own transpose graph, via a special kind of isomorphism that pairs up all of the vertices. The converse relation of a binary relation is the relation that reverses the ordering of each pair of related objects. If the relation is interpreted as a directed graph, this is the same thing as ...
The H-free graphs are the family of all graphs (or, often, all finite graphs) that are H-free. [10] For instance the triangle-free graphs are the graphs that do not have a triangle graph as a subgraph. The property of being H-free is always hereditary. A graph is H-minor-free if it does not have a minor isomorphic to H. Hadwiger 1. Hugo Hadwiger 2.
The different types of edge in a bidirected graph. In the mathematical domain of graph theory, a bidirected graph (introduced by Edmonds & Johnson 1970) [1] is a graph in which each edge is given an independent orientation (or direction, or arrow) at each end. Thus, there are three kinds of bidirected edges: those where the arrows point outward ...
In category theory, a branch of mathematics, an antiisomorphism (or anti-isomorphism) between structured sets A and B is an isomorphism from A to the opposite of B (or equivalently from the opposite of A to B). [1] If there exists an antiisomorphism between two structures, they are said to be antiisomorphic.
The linear–log type of a semi-log graph, defined by a logarithmic scale on the x axis, and a linear scale on the y axis. Plotted lines are: y = 10 x (red), y = x (green), y = log(x) (blue). In science and engineering, a semi-log plot/graph or semi-logarithmic plot/graph has one axis on a logarithmic scale, the other on a linear scale.
The fact that the complement of a perfect graph is also perfect is the perfect graph theorem of László Lovász. [4] Cographs are defined as the graphs that can be built up from single vertices by disjoint union and complementation operations. They form a self-complementary family of graphs: the complement of any cograph is another different ...
The opposite, a graph with only a few edges, is a sparse graph. The distinction of what constitutes a dense or sparse graph is ill-defined, and is often represented by 'roughly equal to' statements. Due to this, the way that density is defined often depends on the context of the problem.
The composition of two automorphisms is another automorphism, and the set of automorphisms of a given graph, under the composition operation, forms a group, the automorphism group of the graph. In the opposite direction, by Frucht's theorem, all groups can be represented as the automorphism group of a connected graph – indeed, of a cubic graph.