翻訳と辞書 Words near each other ・ Edge of Thorns ・ Edge of Tomorrow (film) ・ Edge of Twilight ・ Edge of Twilight (series) ・ Edge of Twilight (video game) ・ Edge of Winter ・ Edge Peak ・ Edge pull ・ Edge Radio ・ Edge recombination operator ・ Edge Rocks ・ Edge routing ・ Edge School ・ Edge Side Includes ・ Edge sorting ・ Edge space ・ EDGE species ・ Edge Springs ・ Edge STP ・ Edge Studio ・ EDGE Tech ・ Edge Technologies ・ Edge Therapeutics ・ Edge TV ・ Edge wave ・ Edge West Productions ・ Edge Wireless ・ Edge, Branscombe ・ Edge, Cheshire ・ Edge, Gloucestershire Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Edge space ： ウィキペディア英語版 Edge space In the mathematical discipline of graph theory, the edge space and vertex space of an undirected graph are vector spaces defined in terms of the edge and vertex sets, respectively. These vector spaces make it possible to use techniques of linear algebra in studying the graph. ==Definition== Let $G:=(V,E)$ be a finite undirected graph. The vertex space $\backslash mathcal(G)$ of ''G'' is the vector space over the finite field of two elements $\backslash mathbb/2\backslash mathbb:=\backslash lbrace\; 0,1\; \backslash rbrace$ of all functions $V\backslash rightarrow\; \backslash mathbb/2\backslash mathbb$. Every element of $\backslash mathcal(G)$ naturally corresponds the subset of ''V'' which assigns a 1 to its vertices. Also every subset of ''V'' is uniquely represented in $\backslash mathcal(G)$ by its characteristic function. The edge space $\backslash mathcal(G)$ is the $\backslash mathbb/2\backslash mathbb$-vector space freely generated by the edge set ''E''. The dimension of the vertex space is thus the number of vertices of the graph, while the dimension of the edge space is the number of edges. These definitions can be made more explicit. For example, we can describe the edge space as follows: * elements of the vector space are subsets of $E$, that is, as a set $\backslash mathcal(G)$ is the power set of ''E'' * vector addition is defined as the symmetric difference: $P+Q:=P\; \backslash triangle\; Q\; \backslash qquad\; P,Q\; \backslash in\; \backslash mathcal(G)$ * scalar multiplication is defined by: * *$0\; \backslash cdot\; P\; :=\; \backslash emptyset\; \backslash qquad\; P\; \backslash in\; \backslash mathcal(G)$ * * $1\; \backslash cdot\; P\; :=\; P\; \backslash qquad\; P\; \backslash in\; \backslash mathcal(G)$ The singleton subsets of ''E'' form a basis for $\backslash mathcal(G)$. One can also think of $\backslash mathcal(G)$ as the power set of ''V'' made into a vector space with similar vector addition and scalar multiplication as defined for $\backslash mathcal(G)$. 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「Edge space」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.