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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 Graph amalgamation ： ウィキペディア英語版 Graph amalgamation In graph theory, a graph amalgamation is a relationship between two graphs (one graph is an amalgamation of another). Similar relationships include subgraphs and minors. Amalgamations can provide a way to reduce a graph to a simpler graph while keeping certain structure intact. The amalgamation can then be used to study properties of the original graph in an easier to understand context. Applications include embeddings,〔Gross, Tucker 1987〕 computing genus distribution,〔Gross 2011〕 and Hamiltonian decompositions. == Definition == Let $G$ and $H$ be two graphs with the same number of edges where $G$ has more vertices than $H$. Then we say that $H$ is an amalgamation of $G$ if there is a bijection $\backslash phi:\; E(G)\; \backslash to\; E(H)$ and a surjection $\backslash psi:\; V(G)\; \backslash to\; V(H)$ and the following hold: * If $x$, $y$ are two vertices in $G$ where $\backslash psi(x)\; \backslash neq\; \backslash psi(y)$, and both $x$ and $y$ are adjacent by edge $e$ in $G$, then $\backslash psi(x)$ and $\backslash psi(y)$ are adjacent by edge $\backslash phi(e)$ in $H$. * If $e$ is a loop on a vertex $x\; \backslash in\; V(G)$, then $\backslash phi(e)$ is a loop on $\backslash psi(x)\; \backslash in\; H$. * If $e$ joins $x,y\; \backslash in\; V(G)$, where $x\; \backslash neq\; y$, but $\backslash psi(x)\; =\; \backslash psi(y)$, then $\backslash psi(e)$ is a loop on $\backslash psi(x)$.〔Hilton 1984〕 Note that while $G$ can be a graph or a pseudograph, it will usually be the case that $H$ is a pseudograph. 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「Graph amalgamation」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.