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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Matching polynomial ： ウィキペディア英語版 Matching polynomial In the mathematical fields of graph theory and combinatorics, a matching polynomial (sometimes called an acyclic polynomial) is a generating function of the numbers of matchings of various sizes in a graph. ==Definition== Several different types of matching polynomials have been defined. Let ''G'' be a graph with ''n'' vertices and let ''mk'' be the number of ''k''-edge matchings. One matching polynomial of ''G'' is :$m\_G(x)\; :=\; \backslash sum\_\; m\_k\; x^k.$ Another definition gives the matching polynomial as :$M\_G(x)\; :=\; \backslash sum\_\; (-1)^k\; m\_k\; x^.$ A third definition is the polynomial :$\backslash mu\_G(x,y)\; :=\; \backslash sum\_\; m\_k\; x^k\; y^.$ Each type has its uses, and all are equivalent by simple transformations. For instance, :$M\_G(x)\; =\; x^n\; m\_G(-x^)$ and :$\backslash mu\_G(x,y)\; =\; y^n\; m\_G(x/y^2).$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Matching polynomial」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.