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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 ...
It has n 2 + 2n + 1 vertices: n 2 formed from the product of a leaf in both factors, 2n from the product of a leaf in one factor and the hub in the other factor, and one remaining vertex formed from the product of the two hubs. Each leaf-hub product vertex in G dominates exactly n of the leaf-leaf vertices, so n leaf-hub vertices are needed to ...
G := set of pages for each page p in G do p.auth = 1 // p.auth is the authority score of the page p p.hub = 1 // p.hub is the hub score of the page p function HubsAndAuthorities(G) for step from 1 to k do // run the algorithm for k steps for each page p in G do // update all authority values first p.auth = 0 for each page q in p ...
Two graphs are homomorphically equivalent if there exist two homomorphisms, one from each graph to the other graph. homomorphism 1. A graph homomorphism is a mapping from the vertex set of one graph to the vertex set of another graph that maps adjacent vertices to adjacent vertices. This type of mapping between graphs is the one that is most ...
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 ...
Clique-sums have a close connection with treewidth: If two graphs have treewidth at most k, so does their k-clique-sum.Every tree is the 1-clique-sum of its edges. Every series–parallel graph, or more generally every graph with treewidth at most two, may be formed as a 2-clique-sum of triangles.
Other pairs of graph types that always admit a simultaneous embedding, but that might need larger grid sizes, include a wheel graph and a cycle graph, a tree and a matching, or a pair of graphs both of which have maximum degree two. However, pairs of planar graphs and a matching, or of a Angelini, Geyer, Neuwirth and Kaufmann showed that a tree ...
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 ...