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Statements

Subject Item

dbr:Graph_polynomial

rdfs:label

Graph polynomial

rdfs:comment

In mathematics, a graph polynomial is a graph invariant whose values are polynomials. Invariants of this type are studied in algebraic graph theory.Important graph polynomials include: * The characteristic polynomial, based on the graph's adjacency matrix. * The chromatic polynomial, a polynomial whose values at integer arguments give the number of colorings of the graph with that many colors. * The dichromatic polynomial, a 2-variable generalization of the chromatic polynomial * The flow polynomial, a polynomial whose values at integer arguments give the number of nowhere-zero flows with integer flow amounts modulo the argument. * The (inverse of the) Ihara zeta function, defined as a product of binomial terms corresponding to certain closed walks in a graph. * The , used by Pierre

dcterms:subject

dbc:Graph_invariants dbc:Polynomials

dbo:wikiPageID

56012962

dbo:wikiPageRevisionID

841879539

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dbr:Reliability_polynomial dbr:Martin_polynomial dbr:Knot_polynomial dbr:Euler_tour dbr:Graph_property dbr:Nowhere-zero_flow dbc:Graph_invariants dbr:Dichromatic_polynomial dbr:Tutte_polynomial dbr:Flow_polynomial dbr:Induced_subgraph dbr:Matching_(graph_theory) dbr:Generating_function dbr:Algebraic_graph_theory dbr:Adjacency_matrix dbr:Matching_polynomial dbc:Polynomials dbr:Characteristic_polynomial dbr:Polynomial dbr:Ihara_zeta_function dbr:Chromatic_polynomial

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dbpedia-hu:Gráfpolinom n13:4XueH wikidata:Q48999599

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dbo:abstract

In mathematics, a graph polynomial is a graph invariant whose values are polynomials. Invariants of this type are studied in algebraic graph theory.Important graph polynomials include: * The characteristic polynomial, based on the graph's adjacency matrix. * The chromatic polynomial, a polynomial whose values at integer arguments give the number of colorings of the graph with that many colors. * The dichromatic polynomial, a 2-variable generalization of the chromatic polynomial * The flow polynomial, a polynomial whose values at integer arguments give the number of nowhere-zero flows with integer flow amounts modulo the argument. * The (inverse of the) Ihara zeta function, defined as a product of binomial terms corresponding to certain closed walks in a graph. * The , used by Pierre Martin to study Euler tours * The matching polynomials, several different polynomials defined as the generating function of the matchings of a graph. * The reliability polynomial, a polynomial that describes the probability of remaining connected after independent edge failures * The Tutte polynomial, a polynomial in two variables that can be defined (after a small change of variables) as the generating function of the numbers of connected components of induced subgraphs of the given graph, parameterized by the number of vertices in the subgraph.

prov:wasDerivedFrom

wikipedia-en:Graph_polynomial?oldid=841879539&ns=0

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1941

foaf:isPrimaryTopicOf

wikipedia-en:Graph_polynomial