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Topic: Graph homomorphism

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	Graph homomorphism - Wikipedia, the free encyclopedia
		In the mathematical field of graph theory a graph homomorphism is a mapping between two graphs that respects their structure.
		If the homomorphism f is a bijection, then the inverse function is also a graph homomorphism, so f is a graph isomorphism.
		In this case, the two graphs are identical from the viewpoint of graph theory.
	en.wikipedia.org /wiki/Graph_homomorphism (391 words)

	Encyclopedia: List of graph theory topics (Site not responding. Last check: 2007-10-22)
		In graph theory, a cocoloring of a graph G is an assignment of colors to the vertices such that each color class forms an independent set in G or the complement of G. The cochromatic number z(G) of G is the least number of colors needed in any cocolorings...
		In graph theory, a perfect graph is a graph in which the chromatic number of every induced subgraph equals the clique number of that subgraph.
		In mathematics, spectral graph theory is the study of properties of a graph in relationship to the eigenvalues and eigenvectors of its adjacency matrix.
	www.nationmaster.com /encyclopedia/List-of-graph-theory-topics (4555 words)

	Graph coloring (Site not responding. Last check: 2007-10-22)
		In graph theory, graph coloring is an assignment of "colors", almost always taken to be consecutive integers starting from 1 without loss of generality, to certain objects in a graph.
		Graph coloring is not to be confused with graph labeling, which is an assignment of labels, usually also in the form of numbers, to vertices or edges.
		The chromatic polynomial of a graph was introduced by Birkhoff and Lewis in their attack on the four-color theorem.
	www.sciencedaily.com /encyclopedia/graph_coloring (933 words)

	Graph homomorphism -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		In the (Click link for more info and facts about mathematical) mathematical field of (Click link for more info and facts about graph theory) graph theory a graph homomorphism is a mapping between two (A drawing illustrating the relations between certain quantities plotted with reference to a set of axes) graphs that respects their structure.
		If the homomorphism is a (Click link for more info and facts about bijection) bijection, then the inverse function is also a graph homomorphism, so is a graph ((biology) similarity or identity of form or shape or structure) isomorphism.
		Graph homomorphism preserve (A relation between things or events (as in the case of one causing the other or sharing features with it)) connectedness and (Click link for more info and facts about diconnectedness) diconnectedness.
	www.absoluteastronomy.com /encyclopedia/g/gr/graph_homomorphism.htm (472 words)

	ipedia.com: Graph coloring Article (Site not responding. Last check: 2007-10-22)
		A 3-coloring of a graph In graph theory, graph coloring is an assignment of "colors", almost always taken to be consecutive integers starting from 1 without loss of generality, to certain objects in a...
		For example the chromatic number of a complete graph of vertices (a graph with an edge between every two vertices), is.
		For example for the complete graph of 3 vertices(), since the first vertex can be colored in ways, the second in ways and so on.
	www.ipedia.com /graph_coloring.html (981 words)

	Graph in TutorGig Encyclopedia
		In mathematics, and, in particular, in graph theory, a rooted graph is a graph mathematics mathematical graph in which one node graph theory is labelled in a special way to distinguish it from the graph..
		In graph theory the complement or inverse of a graph math G math is a graph math H math on the same vertices...
		In graph theory which is an area in mathematics and computer science a labeled graph is a graph mathematics graph with labels assigned to its nodes and edges.
	www.tutorgig.com /es/Graph (1047 words)

	Patrice Ossona de Mendez (Site not responding. Last check: 2007-10-22)
		) have a representation as the intersection graph of Jordan arcs.
		This graph invariant is closely related to constrained orientation properties of minor closed class of graphs and appears to be a natural strengthening of tree-width.
		The study of the relationships existing between poset dimension and homomorphism led Pierre Rosenstiehl and myself to introduce the universal dimension of a graph, the study of which already gave interesting non obvious results on the dimension of the incidence poset of graphs (particularly chromatic and extremal properties).
	www.ehess.fr /centres/cams/person/pom (1044 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).
		The artists László Moholy-Nagy in Berlin, Germany, and Jack Ellit in London, England, were experimenting at this time with freely drawn soundtracks incorporating found images, thumbprints, and so on, of predictable rhythm but noisy character, a technique later adopted by the Canadian film-maker Norman McLaren.
		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.
	encyclopedia.farlex.com /graph+notation (375 words)

	Graph coloring - Freepedia (Site not responding. Last check: 2007-10-22)
		For example the chromatic number of a complete graph of $n$ vertices (a graph with an edge between every two vertices), is $n$ .
		Two colorings of G will be considered different if at least one of the labeled points is assigned a different color.Then, it can be shown that $f(G, t)$ will be a polynomial in $t$ .
		For example for the complete graph of 3 vertices( $K_3$ ), $f(K_3, t) = t(t-1)(t-2)$ since the first vertex can be colored in $t$ ways, the second in $t-1$ ways and so on.
	en.freepedia.org /Chromatic_number.html (995 words)

	Graph isomorphism - Wikipedia, the free encyclopedia
		A graph isomorphism is a bijection between the vertices of two graphs G and H:
		Determining whether two graphs are isomorphic is the graph isomorphism problem
		This article incorporates material from graph isomorphism on PlanetMath, which is licensed under the GFDL.
	en.wikipedia.org /wiki/Graph_isomorphism (122 words)

	Geometry.Net - Pure And Applied Math Books: Graph Theory
		The text can be used in a one semester introductory graduate course in graph theory in a CS or math department, an advanced undergraduate seminar or as a reference book for an undergraduate course in discrete math.
		Gross is a pioneer in voltage graphs and the treatment of this somewhat esoteric subject is lucid and complete.
		--It is sketchy on chromatic polynomial, planar graph.
	www.geometry.net /pure_and_applied_math_bk/graph_theory_page_no_2.html (2829 words)

	Graph - Definition of Graph by Webster's Online Dictionary (Site not responding. Last check: 2007-10-22)
		(Math.) A curve or surface, the locus of a point whose coördinates are the variables in the equation of the locus; as, a graph of the exponential function.
		A diagram symbolizing a system of interrelations of variable quantities using points represented by spots, or by lines to represent the relations of continuous variables.
		More than one set of interrelations may be presented on one graph, in which case the spots or lines are typically distinguishable from each other, as by color, shape, thickness, continuity, etc.
	www.webster-dictionary.org /definition/graphs (184 words)

	Definition of Graph isomorphism
		A graph homomorphism $f from a$ graph $G:=(V,E) to a$ graph $G':=(V',E') is a function$
		If the homomorphism $f is a bijection, then the inverse function is also a$ graph homomorphism, so $f is a$ graph isomorphism.
		A graph H is a subgraph of G if and only if there exists a monomorphism $f:H\to G .$
	www.wordiq.com /definition/Graph_isomorphism (406 words)

	Some problems (Site not responding. Last check: 2007-10-22)
		Input: A planar graph G=(V,E) and an integer valued function f on the vertex set of G. Output: An orientation of G such that the indegree of any vertex x is at most f(x), if such an orientation exists.
		The reduced genus of a multigraph G is the minimum of the genus of the vertex-edge incidence graph of a hypergraph having the same adjacencies as G with the same multiplicities.
		The universal dimension udim G of a graph G is the supremum of the dimensions of the incidence posets of the graphs having a homomorphism to G:
	www.ehess.fr /centres/cams/person/pom/langen/openpb.html (626 words)

	Biopathways Graph Data Manager (BGDM)
		I have broad interests in graphs, their role in databases and knowledge representation, graph algorithms (esp. parallel graph algorithms) for biology (phylogenetic tree construction, NMR peak assignment, shotgun sequence assembly, etc.), and graph grammars (for modeling graph query languages, evolution of biopathways, schema evolution and integration).
		subgraph homomorphism queries (similar to subgraph isomorphism, except that the labels on the query subgraph nodes are generalizations of the terms used to label nodes in the database (i.e., taken from a concept lattice or taxonomy).
		Graph matchings attempt to match entire graphs and are the graph analogs of global sequence alignments.
	www.lbl.gov /~olken/graphdm/graphdm.htm (7829 words)

	2002 Summer Research Conference-Graph Coloring and Symmetry
		The workshop will focus on applications of results from the theory of symmetric functions to graph homomorphism problems and to the development of graph-coloring algorithms, and applications of tools from the theory of graph homomorphisms and graph-coloring algorithms to illuminate the theory of symmetric functions.
		A typical example well known to all graph theorists is the following fact, implied by the theorem of Brooks: While three-colouring is NP-complete in general, it is polynomial time solvable for graphs with degrees bounded by three, but NP-complete again if the degree bound is changed to four.
		The circular flow number \Phi_c(G) of a graph G is the least p/q such that G admits a (p, q)-flow.
	kcollins.web.wesleyan.edu /2002graphs-a-symmetry.htm (747 words)

	Workshop on Data Management for Molecular and Cell Biology
		Graphs are used to represent metabolic pathways, signaling pathways, genetic control networks, various physical and genetic maps (partial orders), concept lattices, chemical structure graphs, 3D chemical structures, etc. Although graphs can be encoded into relational DBMSs, few relational DBMSs have good facilities for querying graph structures.
		Graph queries are often recursive, and may involve subgraph isomorphism queries (for chemical structure graphs), or graph homomorphism queries (of metabolic pathways).
		While a few DBMSs support recursive queries, subgraph isomorphism or graph homomorphism queries are generally not supported at all, much less with convenient query languages.
	www.lbl.gov /~olken/wdmbio/wsproposal1.htm (4519 words)

	Exmo research pages
		Though the graphical representation of these objects is often considered as an interesting feature for knowledge representation (natural representation, intuitive understanding), we are most interested in graphs as a mathematical structure, and in their use for reasoning.
		Coming from a conceptual graph background, we have adapted the reasoning operation used in this model (basically a graph homomorphism) to obtain sound and complete inferences in the Semantic Web languages RDF [Baget 2003c] and RDFS.
		Querying RDF graphs can be reduced to computing entailment and a popular way to compute entailment is to find a projection from an RDF graph to another.
	www.inrialpes.fr /exmo/research/proptrans.html (2255 words)

	math lessons - Category:Graph theory (Site not responding. Last check: 2007-10-22)
		Graph theory is the branch of mathematics that examines the properties of graphs.
		See glossary of graph theory for common terms and their definition.
		Informally, a graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs).
	www.mathdaily.com /lessons/Category:Graph_theory (86 words)

	Citations: Pultr: On classes of relations and graphs determined by subobjects and factorobjects - Nesetril ... (Site not responding. Last check: 2007-10-22)
		....graph used to represent B in Sections 2, 5, 6 and 7.
		....H colourable graphs (that is, graphs G for which there is a homomorphism G H) for any non bipartite graph H.
		Then the class H = fG j there is a homomorphism G Hg is an FGH class.
	citeseer.ist.psu.edu /context/665163/0 (437 words)

	Read about Category:Graph theory at WorldVillage Encyclopedia. Research Category:Graph theory and learn about ... (Site not responding. Last check: 2007-10-22)
		glossary of graph theory for common terms and their definition.
		Informally, a graph is a set of objects called
		Typically, a graph is depicted as a set of dots (i.e., vertices) connected by lines (i.e., edges).
	encyclopedia.worldvillage.com /s/b/Category:Graph_theory (80 words)

	Tutorial on Graph Data Management for Biology
		This tutorial introduce students to graph data management technology for biological applications, with an emphasis on applications to biopathways data, i.e., metabolic pathways, signal transduction pathways, and genetic regulatory networks.
		The tutorial will cover graph data models, graph queries, graph query languages, implementation strategies, history of graph data management systems, examples of current biopathways database systems, comparison to other types of database management systems such as relational, logic and object oriented database systems, and possibly a brief mention of the potential role graph grammars.
		The intended audience is for graduate students, researchers and practicioners in bioinformatics, data management, and graph algorithms, and computer-savvy biologists interested in data management of graph-based biological data: biopathways data, protein interactions networks, chemical structure graphs, phylogenetic trees, etc.
	www.iscb.org /ismb2004/tutorials/olkenATlbl.gov_46.htm (657 words)

	Knowledge Representation and Reasonings Based on Graph Homomorphism (Site not responding. Last check: 2007-10-22)
		The main conceptual contribution in this paper is to present an approach to knowledge representation and reasonings based on labeled graphs and labeled graph homomorphism.
		It is then shown that the basic deduction problem on simple graphs is essentially the same problem as conjunctive query containment in databases and constraint satisfaction; polynomial parsimonious transformations between these problems are exhibited.
		Grounded on the simple graphs model, a knowledge representation and reasoning model allowing to deal with facts, production rules, transformation rules, and constraints is presented, as an illustration of the graph-based approach.
	www.lirmm.fr /~cogito/abstracts/mugniericcs00.html (150 words)

	Automorphism
		Very informally, an automorphism is a symmetry of the object, a way of showing its internal regularity (whichever side of a regular polygon you choose as it basis, it looks the same).
		For example, in graph theory an automorphism of a graph is a permutation of the nodes that maps the graph to itself.
		In group theory, an automorphism of a group G is a bijective homomorphism of G onto itself (that is, a one-to-one map G
	www.fact-index.com /a/au/automorphism_1.html (320 words)

	SAV - -
		We define the $k$@-diameter of a graph as the maximum distance of a set of $k$ vertices; so the $2$@-diameter is the normal diameter and the $n$@-diameter, where $n$ is the order, is the distance of the graph.
		The aim of the paper is to study mappings of partial monounary algebras that respect their graph representation.
		The idea is based on the notion of strong homomorphisms of graphs.
	www.sav.sk /index.php?lang=sk&charset=ascii&doc=publish-journal&part=list_articles&journal_issue_no=1155 (993 words)

	DIMACS/DIMATIA/Renyi Working Group on Algebraic and Geometric Methods in Combinatorics
		Close connections between percolation and random graphs, between graph homomorphisms and hard-constraint models, and between slow mixing and phase transition, have led to new results and new perspectives.
		This work was part of a plan to study combinatorial versions of concepts from statistical physics, and in particular to link graph properties which view a graph as the target of a homomorphism to others in which it is the source, and we shall pursue this plan.
		A geometric graph is a graph drawn in the plane so that the vertices are represented by points in general position and the edges are represented by straight line segments connecting the corresponding points.
	dimacs.rutgers.edu /Workshops/Algebraic/main.html (2719 words)

	baget02a Abstract (Site not responding. Last check: 2007-10-22)
		Abstract: Simple conceptual graphs are considered as the kernel of most knowledge representation formalisms built upon Sowa's model.
		Reasoning in this model can be expressed by a graph homomorphism called projection, whose semantics is usually given in terms of positive, conjunctive, existential FOL.
		We present here a family of extensions of this model, based on rules and constraints, keeping graph homomorphism as the basic operation.
	www.jair.org /abstracts/baget02a.html (184 words)

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