Search results
Results From The WOW.Com Content Network
In general, a subdivision of a graph G (sometimes known as an expansion [2]) is a graph resulting from the subdivision of edges in G. The subdivision of some edge e with endpoints {u,v } yields a graph containing one new vertex w, and with an edge set replacing e by two new edges, {u,w } and {w,v }. For directed edges, this operation shall ...
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 ...
The complement graph ¯ of a simple graph G is another graph on the same vertex set as G, with an edge for each two vertices that are not adjacent in G. complete 1. A complete graph is one in which every two vertices are adjacent: all edges that could exist are present. A complete graph with n vertices is often denoted K n.
Graphlets in mathematics are induced subgraph isomorphism classes in a graph, [1] [2] i.e. two graphlet occurrences are isomorphic, whereas two graphlets are non-isomorphic. . Graphlets differ from network motifs in a statistical sense, network motifs are defined as over- or under-represented graphlets with respect to some random graph null m
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.
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
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]
Switching {X,Y} in a graph. A two-graph is equivalent to a switching class of graphs and also to a (signed) switching class of signed complete graphs.. Switching a set of vertices in a (simple) graph means reversing the adjacencies of each pair of vertices, one in the set and the other not in the set: thus the edge set is changed so that an adjacent pair becomes nonadjacent and a nonadjacent ...