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Topic: Graph isomorphism

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graph theory

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graph of a function

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	PlanetMath: graph isomorphism
		A graph isomorphism is a bijection between the vertices of two graphs
		If an isomorphism can be constructed between two graphs, then we say those graphs are isomorphic.
		This is version 2 of graph isomorphism, born on 2002-02-03, modified 2002-02-03.
	planetmath.org /encyclopedia/GraphIsomorphism.html (66 words)

	[No title]
		While most articles related to graph isomorphism have been published in the computer science literature, the computation of the orbits of automorphism groups using partitioning techniques has received most attention in chemistry.
		However, in the context of chemistry because molecules are a restricted class of graphs, we have proven the problems of graph isomorphism, automorphism partitioning, and canonical labeling to be polynomial-time.
		A molecular graph is a multigraph without loop (an atom is not bonded to itself) colored by the elements of the periodic table.
	www.cs.sandia.gov /~jfaulon/MICS/isomorphism/isomorphism.html (610 words)

	Graph homomorphism - Wikipedia, the free encyclopedia
		In the mathematical field of graph theory a graph homomorphism is a mapping between two graphs that respect their structure.
		is a bijection whose inverse function is also a graph homomorphism, then f is a graph isomorphism.
		Determining whether there is an isomorphism between two graphs is an important problem in computational complexity theory; see graph isomorphism problem.
	en.wikipedia.org /wiki/Graph_homomorphism (273 words)

	GRAPH ISOMORPHISM PROBLEM: AN ALGORITHM FOR SOLUTION
		The graph isomorphism problem can not be placed in any of known complexity classes as it was stated in [1].
		The isomorphism of the graphs checks at most at n iterations of the algorithm, where n is a number of vertices of graphs.
		It is shown that this is holds regardless of maximal degree of the graphs, graphs genus, graph eigenvalue multiplicity etc., i.e., using the algorithm, solution of the graph isomorphism problem has no specific that may be determinate by any graph characteristics that is usually considered.
	www.psy.omsu.omskreg.ru /session/isomorphism (501 words)

	Graph Isomorphism (Site not responding. Last check: 2007-10-26)
		The problem of deciding algorithmically whether two graphs are isomorphic or structurally equivalent is known as the graph isomorpism problem.
		Two graphs are said to be isomorphic when they are structurally equivalent irrespective of the vertex labels.
		Isomorphic graphs are related by permutation of vertex labels.
	monod.biomath.nyu.edu /rna/tutorials/graph_ismorphism.html (196 words)

	05C: Graph theory
		A graph is a set V of vertices and a set E of edges -- pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on sets, which is clearly a broad topic.
		A graph may be viewed as a one-dimensional CW-complex and hence studied with tools from Algebraic Topology, in particular, questions of planarity (and genus).
		Determining the genus of a graph is NP-complete.
	www.math.niu.edu /~rusin/known-math/index/05CXX.html (1204 words)

	Boost Graph Library: Isomorphism
		An isomorphism is a 1-to-1 mapping of the vertices in one graph to the vertices of another graph such that adjacency is preserved.
		Also, if a isomorphism map named parameter is provided then an isomorphism is recorded in the map.
		BinaryFunction where the first argument is a vertex descriptor, the second argument is a graph, and the result type is an integer.
	www.boost.org /libs/graph/doc/isomorphism.html (337 words)

	[No title]
		Graph Grammars and Their Application to Computer Science}, publisher = {Springer-Verlag}, pages = {174--189}, year = {1990}, abstract = {The paper is concerned with the efficient determination of the set of productions of a graph grammar that are applicable in one rewriting step.
		Subsequently, subgraph isomorphism is considered as a special case of graph similarity and a new efficient algorithm for its detection is proposed.
		New graphs can be encoded at run time without recompiling the whole hierarchy: having found a graph's structural type, the authors then use it to hash to the code encoding the poset of all possible type-labeled graphs ordered by subsumption.
	www.ics.uci.edu /~eppstein/bibs/subiso.bib (13928 words)

	Part 1
		For example, for some large graphs of 5000 vertices almost 99% of the execution time of the entire program was spent in generating the graphs whereas only 1% time was spent in actually finding the isomorphism.
		Also it will be notes as opposed graphs of type A, for type C graphs which are large a majority of the running time is spent in solving the isomorphism problem than generating the graph.
		It is not until we enter the large graphs that we actually see a uniform increase in running time with respect to the number of vertices.
	www.cs.rice.edu /~qasem/projects/graphis.html (1723 words)

	graph notation - Hutchinson encyclopedia article about graph notation
		A form of graph notation for speech patterns used in phonetics was adopted by Karlheinz Stockhausen in Carré/Squared (1959–60).
		John Cage's graphic scores of the 1950s revive memories of film experiments in the 1930s, as may be said of many European composers of graph scores from the period 1959–70.
		This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.
	encyclopedia.farlex.com /graph+notation (375 words)

	BindView - Comparing binaries with graph isomorphisms (Site not responding. Last check: 2007-10-26)
		In terms of comparing binaries, the vertices of the graphs would be instructions and constant data like strings, call tables, etc. The edges of the graphs would be edges from the function flow graphs and references made by instructions to constant data.
		The graph is directed, and most of the nodes in the graph have only one incoming edge and one outgoing edge.
		This occurs because those blocks are on a part of the graph that can only be reached by going through earlier parts of the graph that were not isomorphic.
	www.bindview.com /Services/Razor/Papers/2004/comparing_binaries.cfm (4899 words)

	Chris Rafuse: Graph Isomorphism Bonus Assignment
		This object is used by other object to determine graph isomorphism.
		graph two is reconstructed from the new node order and compared to graph one.
		Nodes within the recorded intervals for graph two are permuted lexigraphically according to their node number (note: since the intervals contain only nodes with same number of degrees, nodes with unique degrees are not included in permutation)
	torch.cs.dal.ca /~crafuse/IsomorphDoc.htm (516 words)

	Graph Isomorphism
		Subgraph isomorphism asks whether there is a subset of edges and vertices of G that is isomorphic to a smaller graph H.
		Polynomial-time algorithms are known for planar graph isomorphism [HW74] and for graphs where the maximum vertex degree is bounded by a constant [Luk80].
		Testing the isomorphism of bipartite graphs is isomorphism-complete, since any graph can be made bipartite by replacing each edge by two edges connected with a new vertex.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE180.HTM (1415 words)

	[No title] (Site not responding. Last check: 2007-10-26)
		Yes, it is still open whether graph isomorphism is NP-complete.
		it is known that the NP-completeness of graph isomorphism would imply that the polynomial hierarchy collapses to its second level (which is considered to be a very unlikely event).
		Graph isomorphism lies in co-NP and also in some probabilistically enhanced version of NP.
	www.math.niu.edu /~rusin/known-math/99/graph_iso (387 words)

	Project Links \| Graph Isomorphism (Site not responding. Last check: 2007-10-26)
		Clearly, the uncolored graph isomorphism problem is a special case of the colored one: if and are two uncolored graphs, then we can always assign to every vertex and every edge the same color which transfers the pair of graphs into a pair of color graphs.
		Surprisingly, the colored graph isomorphism problem can be reduced to the uncolored graph isomorphism problem by a suitable transformation of the input colored graphs into corresponding uncolored graphs.
		First, notice that if the colors used for one graphs are different from that of the other graphs, then the graphs are non-isomorphic.
	links.math.rpi.edu:16080 /devmodules/graph_isomorphism/html/Transform.html (298 words)

	Fast Error-correcting Graph Isomorphism Based on Model Precompilation — IAM
		The new algorithm is an extension of a method for exact subgraph isomorphism detection from an input graph to a set of a priori known model graphs, which was previously developed by the authors.
		At run time, it is used to find all error-correcting graph isomorphisms from an input graph to any of the model graphs up to a certain degree of distortion.
		The main advantage of the new algorithm is that error-correcting graph isomorphism detection is guaranteed to require time that is only polynomial in terms of the size of the input graph.
	www.iam.unibe.ch /publikationen/techreports/1996/iam-96-012 (274 words)

	Comp.compilers: Re: On CFL equivalence and graph isomorphism
		Re: On CFL equivalence and graph isomorphism lex@cc.gatech.edu (2000-04-25)
		Re: On CFL equivalence and graph isomorphism pmoisset@altavista.net (Pablo) (2000-04-25)
		graphs are not isomorphic then the grammars are not equivalent.
	compilers.iecc.com /comparch/article/00-04-168 (421 words)

	Graph Theory Lesson 3
		If two graphs are isomorphic then as far as we are concerned they are the same graph though the location of the vertices may be different.
		To show you how the program can be used to explore isomorphism draw the graph in figure 4 with the program (first get the null graph on four vertices and then use the right mouse to add edges).
		When two graphs are isomorphic we consider them to be the same graph.
	oneweb.utc.edu /~Christopher-Mawata/petersen/lesson3.htm (421 words)

	Project Links \| Graph Isomorphism (Site not responding. Last check: 2007-10-26)
		A naive approach to solving the graph isomorphism problems is to look at the Adjacency Matrix of each graph.
		If they are identical, then the graphs are isomorphic, with a trivial mapping of vertices.
		By renumbering the vertices of the graph, we affect the corresponding adjacency matrices of the graph.
	links.math.rpi.edu:16080 /devmodules/graph_isomorphism/html/Adjacency.html (83 words)

	Algorithmic Solutions Software GmbH: LEDA
		Subgraph isomorphism and graph monomorphism are known to be NP-complete, the reduction of CLIQUE to either one is trivial....'
		Read the paper Graph Isomorphism Implementation in LEDA 5.1 for more details, have a look in the 5.1 manual and play around with the demo program demo/graph_iso/gw_isomorphism.cpp (part of your LEDA package).
		Finally static graphs support several efficient ways - efficient compared to using node_arrays, edge_arrays, node_maps, and edge_maps - to associate data with the edges and nodes of the graph.
	www.algorithmic-solutions.com /enleda.htm (784 words)

	Graph Isomorphism in Expected Linear Time and Space, March-2005 (Site not responding. Last check: 2007-10-26)
		Abstract: We present an algorithm for testing if two graphs are isomorphic and give evidence that its time and space complexity are, on average, linear in the number of nodes and edges in the graphs being compared.
		We demonstrate results on random graphs, and on non-random graphs with a significant amount of symmetry.
		Our experiments show that these results hold even when the graphs are sparse, i.e., in cases where the number of edges in the graph is O(N), the number of nodes in the graph.
	www.iona.edu /cs/faculty/FacultyPublications/GraphIsoMar30-05abstract.htm (173 words)

	Graph Theory Lesson 3 (Site not responding. Last check: 2007-10-26)
		If two graphs are isomorphic then as far as we are concerned they are the same graph though the location of the vertices may be different.
		To show you how the program can be used to explore isomorphism draw the graph in figure 4 with the program (first get the null graph on four vertices and then use the right mouse to add edges).
		When two graphs are isomorphic we consider them to be the same graph.
	www.utc.edu /~cpmawata/petersen/lesson3.htm (421 words)

	REFERENCE: (Site not responding. Last check: 2007-10-26)
		Informally, the graph isomorphism problem is take two graphs and calculate whether they are "the same." Before tacking the general problem, we'll consider a simple version of an alorithm for finding an isomorphism on trees, a subclass of graphs, (Justin will demonstrate a probabilistic algorithm.)
		takes node 1 in the first graph to node 1 in the second graph, 2 to 5, 3 to 3, 4 to 4, 5 to 2, and 6 to 6, i.e.
		Then it compares the neighbors of the leaves of the two graphs and so on until we find that the trees are the isomorphic or not.
	www.reed.edu /academic/math442/mattiso.html (822 words)

	A global constraint for graph isomorphism problem (Site not responding. Last check: 2007-10-26)
		Graphs provide a rich mean for modeling structured objects and they are widely used in real-life applications to represent, e.g., molecules, images, or networks.
		In many of these applications, one has to compare graphs to decide if their structure is identical.
		This problem is known as the Graph Isomorphism Problem (GIP).
	liris.cnrs.fr /sebastien.sorlin/A_global_constraint_for_graph_isomorphism_problems.html (86 words)

	CS345: Project on graph isomorphism (Site not responding. Last check: 2007-10-26)
		It is, given a graph G and a graph g, to verify whether "G has a subgraph which is isomorphic to g" or not.
		But for some special cases (if G is a tree or planar), it had been shown that, subgraph isomorphism problem can be solved in polynomial time.
		But in real world applications graphs may not be trees(or planar) always.So the current research interest is to develop some heuristic algorithms for such NP-complete problems, which have high probability of success.
	www.cse.iitk.ac.in /users/dsrkg/cs245/html/proj2.htm (139 words)

	Graph isomorphism (Site not responding. Last check: 2007-10-26)
		are equivalent except for their labeling by saying they are isomorphic.
		We consider graphs up to isomorphism, that is we consider isomorphic graphs to be equivalent, and a property that we prove about one is true of the other.
		Even though there are many isomorphisms, they are all equivalent.
	www.cs.toronto.edu /~heap/270F02/node34.html (140 words)

	NAUTY -- Graph Isomorphism (Site not responding. Last check: 2007-10-26)
		Nauty (No AUTomorphisms, Yes?) is a set of very efficient C language procedures for determining the automorphism group of a vertex-colored graph.
		Nauty is also able to produce a canonically-labeled isomorph of the graph, to assist in isomorphism testing.
		It was the basis of the first program to generate all the 11-vertex graphs without isomorphs, and can test most graphs of less than 100 vertices in well under a second.
	www.cs.sunysb.edu /~algorith/implement/nauty/implement.shtml (163 words)

	Publikace
		The graph isomorphism problem is very simple to define and understand.
		Efficiency (time complexity) of all practically usable graph isomorphism algorithms is the main issue of the graph isomorphism problem.
		In this paper, we show several graph isomorphism algorithms and, at the end of the paper, we discuss graph isomorphism problem in the context of object-oriented Petri nets, which are a subject of our research.
	www.fit.vutbr.cz /research/view_pub.php?id=6047 (169 words)

	Advogato: Personal info for Bram
		After much cogitation, I think I've figured out some examples of graph isomorphism problems which are almost tricky.
		Take a graph for which for every pair of nodes (X, Y) the entire graph can be mapped onto itself in an isomorphism such that X maps onto Y. There are many example of these, such as hypercubes.
		Then, 'split' each node to make a new graph, such that for each node X in the old graph, there are two nodes in the new graph Y and Y', with Y connected to Y'.
	www.advogato.org /person/Bram (2191 words)

	Homeomorphism of 2-complexes is equivalent to graph isomorphism (Site not responding. Last check: 2007-10-26)
		Homeomorphism of 2-complexes is equivalent to graph isomorphism
		We show that graph isomorphism can be reduced efficiently to 2-complex homeomorphism, and that Whittlesey's criterion can be reduced efficiently to graph isomorphism.
		Therefore graph isomorphism and 2-complex homeomorphism are polynomial-time equivalent.
	www.maths.tcd.ie /report_series/abstracts/tcdm9804.html (61 words)

	A graph isomorphism algorithm
		This document describes a preliminary release of the C++ implementation of VF, an efficient graph isomorphism algorithm decribed in [1].
		is used to find all the isomorphisms, and rep is a repetition count, used to repeat the matching operations for a number of times sufficient to require a time interval which can be measured with enough precision by the system clock.
		This program is used to randomly generate pairs of isomorphic graphs with a given number of nodes and branches.
	msdlocal.ebi.ac.uk /docs/vf (639 words)

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