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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 homomorphism ： ウィキペディア英語版 Graph homomorphism In the mathematical field of graph theory a graph homomorphism is a mapping between two graphs that respects their structure. More concretely it maps adjacent vertices to adjacent vertices. ==Definitions== A graph homomorphism $f$ from a graph $G=(V,E)$ to a graph $G\text{'}=(V\text{'},E\text{'})$, written $f:G\; \backslash rightarrow\; G\text{'}$, is a mapping $f:V\; \backslash rightarrow\; V\text{'}$ from the vertex set of $G$ to the vertex set of $G\text{'}$ such that $\backslash \backslash in\; E$ implies $\backslash \backslash in\; E\text{'}$. The above definition is extended to directed graphs. Then, for a homomorphism $f:G\; \backslash rightarrow\; G\text{'}$, $(f(u),f(v))$ is an arc of $G\text{'}$ if $(u,v)$ is an arc of $G$. If there exists a homomorphism $f:G\backslash rightarrow\; H$ we shall write $G\backslash rightarrow\; H$, and $G\backslash not\backslash rightarrow\; H$ otherwise. If $G\backslash rightarrow\; H$, $G$ is said to be homomorphic to $H$ or $H$-colourable. If the homomorphism $f:G\backslash rightarrow\; G\text{'}$ is a bijection whose inverse function is also a graph homomorphism, then $f$ is a graph isomorphism. Two graphs $G$ and $G\text{'}$ are homomorphically equivalent if $G\backslash rightarrow\; G\text{'}$ and $G\text{'}\backslash rightarrow\; G$. A retract of a graph $G$ is a subgraph $H$ of $G$ such that there exists a homomorphism $r:G\backslash rightarrow\; H$, called retraction with $r(x)=x$ for any vertex $x$ of $H$. A core is a graph which does not retract to a proper subgraph. Any graph is homomorphically equivalent to a unique core. 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 homomorphism」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.