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Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph. A related problem is to find a partition that is optimal terms ...
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 ...
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A set of graphs isomorphic to each other is called an isomorphism class of graphs. The question of whether graph isomorphism can be determined in polynomial time is a major unsolved problem in computer science, known as the graph isomorphism problem. [1] [2] The two graphs shown below are isomorphic, despite their different looking drawings.
The algorithmic problem of model checking concerns testing whether a given graph models a given sentence. The algorithmic problem of satisfiability concerns testing whether there exists a graph that models a given sentence. Although both model checking and satisfiability are hard in general, several major algorithmic meta-theorems show that ...
Graphs are commonly used to encode structural information in many fields, including computer vision and pattern recognition, and graph matching, i.e., identification of similarities between graphs, is an important tools in these areas. In these areas graph isomorphism problem is known as the exact graph matching. [47]
A graph structure can be extended by assigning a weight to each edge of the graph. Graphs with weights, or weighted graphs, are used to represent structures in which pairwise connections have some numerical values. For example, if a graph represents a road network, the weights could represent the length of each road.
An example for an undirected Graph with a vertex r and its corresponding level structure For the concept in algebraic geometry, see level structure (algebraic geometry) In the mathematical subfield of graph theory a level structure of a rooted graph is a partition of the vertices into subsets that have the same distance from a given root vertex.