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dc.contributor.author游鎮魁zh_TW
dc.contributor.author翁志文zh_TW
dc.contributor.authorEu, Zhen-Kuien_US
dc.contributor.authorWeng, Chih-Wenen_US
dc.date.accessioned2018-01-24T07:43:29Z-
dc.date.available2018-01-24T07:43:29Z-
dc.date.issued2016en_US
dc.identifier.urihttp://etd.lib.nctu.edu.tw/cdrfb3/record/nctu/#GT070352229en_US
dc.identifier.urihttp://hdl.handle.net/11536/143485-
dc.description.abstract對一無向圖形 G,令 E(v) 記為圖形中頂點 v 的相鄰邊所構成之集合。圖 G 上一零和流為一組對邊的非零實數編號 f 使得對每一頂點 v 來說, ∑ f (e) = 0 e∈E(v) 皆成立。 零和 k-流為一零和流且編號全來自集合{±1,...,±(k−1)}。 零和流數 F(G) 定義為圖 G 具有零和 k-流之最小正整數 k。在此篇論文中,對一(2,3)-圖形 G 給出了具有零和流數 3 的充分且必要之條件。此外我們研究由路徑和樹擴展而成之(2,3)-圖形上的零和流數,名曰,聖誕燈、樹燈,並總結它們的零和流數最多為 5。zh_TW
dc.description.abstractFor an undirected graph G, let E(v) denote the set of edges incident on a vertex v ∈ V(G). A zero-sum flow is an assignment f of non-zero real numbers on the edges of G such that ∑ f (e) = 0 e∈E(v) for all v ∈ V(G). A zero-sum k-flow is a zero-sum flow with integers from the set {±1,...,±(k−1)}. Let zero-sum flow number F(G) be defined as the least number of k such that G admits a zero-sum k-flow. In this paper, a necessary and sufficient condition for (2,3)-graph G with F(G) = 3 is given. Furthermore we study zero-sum flow number of (2,3)-graphs expanded from path and tree, namely, the Christmas lamps, the tree lamps, respectively, and conclude that their zero-sum flow numbers are at most 5.en_US
dc.language.isoen_USen_US
dc.subject零和流zh_TW
dc.subject零和 k-流zh_TW
dc.subject零和流數zh_TW
dc.subject(2,3)-圖形zh_TW
dc.subject聖誕燈zh_TW
dc.subject樹燈zh_TW
dc.subjectzero-sum flowen_US
dc.subjectzero-sum k-flowen_US
dc.subjectzero-sum flow numberen_US
dc.subject(2,3)-graphen_US
dc.subjectChristmas lampen_US
dc.subjecttree lampen_US
dc.title關於(2,3)-圖形零和流數之研究zh_TW
dc.titleZero-Sum Flow Numbers of (2,3)-Graphsen_US
dc.typeThesisen_US
dc.contributor.department應用數學系所zh_TW
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