DC FieldValueLanguage
dc.contributor.author許純寧zh_TW
dc.contributor.author傅恆霖zh_TW
dc.contributor.authorHsu, Chuen-Ningen_US
dc.contributor.authorFu, Hung-Linen_US
dc.date.accessioned2018-01-24T07:40:06Z-
dc.date.available2018-01-24T07:40:06Z-
dc.date.issued2017en_US
dc.identifier.urihttp://etd.lib.nctu.edu.tw/cdrfb3/record/nctu/#GT070452220en_US
dc.identifier.urihttp://hdl.handle.net/11536/141038-
dc.description.abstract維納指數是指一個圖形中所有點之間的距離總和，在圖論領域已經進行了廣泛的研究。雖然有不少的圖類，我們可以正確地算出它們的維納指數，可是就一般圖而言，計算維納指數是非常困難的工作。從文獻中，我們不難發現圖中的某一邊 e 扮演重要角色，也就是說能算去掉 e 前後的差值以及去掉邊之後的維納指數，就可以正確算出圖的維納指數。在本論文中，我們首先對特殊的合成圖，如連結圖、合成圖及乘積圖等做研究，算出可能的差值，最後就一般圖估計這變化的差值的上界。zh_TW
dc.description.abstractLet G be a connected graph and d_{G}(u,v) denote the distance between two vertices u and v in V(G). Then the Wiener index of G denoted by W(G) is the total sum of all distances between two vertices in V(G), i.e. W(G) = Σ_{{x,y}⊆V(G)}d_G(x,y). Even there are quite a few classes of graphs G, W(G) is known. But, in general, computing W(G) is very difficult. From the literature, we observe that if we can obtain W(G-e) for certain e∈E(G) and the difference between W(G) and W(G-e), then we have W(G). Therefore, it is interesting to find the difference mentioned above. In this thesis, we first consider several types of composite graphs G such as join graphs, composition graphs and product graphs, and find the difference between W(G) and W(G-e) for all edges e as long as G-e is connected. Furthermore, an estimation of the upper bound on the difference for general graphs in obtained.en_US
dc.language.isoen_USen_US
dc.subject維納指數zh_TW
dc.subject圖形上的距離zh_TW
dc.subject合成圖zh_TW
dc.subject連結圖zh_TW
dc.subject乘積圖zh_TW
dc.subject笛卡爾積圖zh_TW
dc.subject單環圖zh_TW
dc.subjectWiener indexen_US
dc.subjectdistances of graphen_US
dc.subjectjoin graphen_US
dc.subjectcomposition graphen_US
dc.subjectCartesian (square) producten_US
dc.subjectcluster (rooted product)en_US
dc.subjectcoronaen_US
dc.subjectunicyclic graphen_US
dc.title透過刪邊來研究圖的維納指數zh_TW
dc.titleA Study of Wiener Index via Deleting Edgesen_US
dc.typeThesisen_US
dc.contributor.department應用數學系所zh_TW
Appears in Collections:Thesis