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In graph theory and theoretical computer science, a maximum common induced subgraph of two graphs G and H is a graph that is an induced subgraph of both G and H, and that has as many vertices as possible. Finding this graph is NP-hard. In the associated decision problem, the input is two graphs G and H and a number k.
In graph theory, two graphs and ′ are homeomorphic if there is a graph isomorphism from some subdivision of to some subdivision of ′.If the edges of a graph are thought of as lines drawn from one vertex to another (as they are usually depicted in diagrams), then two graphs are homeomorphic to each other in the graph-theoretic sense precisely if their diagrams are homeomorphic in the ...
The image of a function f(x 1, x 2, …, x n) is the set of all values of f when the n-tuple (x 1, x 2, …, x n) runs in the whole domain of f.For a continuous (see below for a definition) real-valued function which has a connected domain, the image is either an interval or a single value.
Subgraph isomorphism is a generalization of the graph isomorphism problem, which asks whether G is isomorphic to H: the answer to the graph isomorphism problem is true if and only if G and H both have the same numbers of vertices and edges and the subgraph isomorphism problem for G and H is true. However the complexity-theoretic status of graph ...
G A variable often used to denote a graph. genus The genus of a graph is the minimum genus of a surface onto which it can be embedded; see embedding. geodesic As a noun, a geodesic is a synonym for a shortest path. When used as an adjective, it means related to shortest paths or shortest path distances. giant
For instance, if G and H are both connected graphs, each having at least four vertices and having exactly twice as many total vertices as their domination numbers, then γ(G H) = γ(G) γ(H). [2] The graphs G and H with this property consist of the four-vertex cycle C 4 together with the rooted products of a connected graph and a single edge.
The modular product of graphs. In graph theory, the modular product of graphs G and H is a graph formed by combining G and H that has applications to subgraph isomorphism.It is one of several different kinds of graph products that have been studied, generally using the same vertex set (the Cartesian product of the sets of vertices of the two graphs G and H) but with different rules for ...
This two-graph is a regular two-graph since each pair of distinct vertices appears together in exactly two triples. Given a simple graph G = (V,E), the set of triples of the vertex set V whose induced subgraph has an odd number of edges forms a two-graph on the set V. Every two-graph can be represented in this way. [1]