發(fā)布時間：2019-01-05 06:07

【摘要】：本文中所涉及的所有的圖均為簡單的無向連通圖。連通圖G的兩個頂點u和v之間的距離dG(u,v)定義為u和v之間的最短路的長度,而u的離心率eccG(u)是指u到圖G中其他所有點的最大距離。連通圖G的中心集C(G)和邊緣集P(G)分別由具有最小離心率和最大離心率的頂點組成的集合。著|C(G)| = |V(G) | - 2 ,稱圖G為幾乎自中心圖(almost self-centered graph,簡記ASC 圖)。若|P(G)| = |V(G)| -1,稱圖 G為幾乎邊緣圖(almost-peripheral graph,簡記 AP圖)。本文分別研究幾乎自中心圖和幾乎邊緣圖的極值問題。第一章簡單介紹了本文中所涉及圖的一些基本的概念、符號和相關(guān)的研究背景,并且給出了AS 圖和AP圖的相關(guān)定義。第二章給出階為n的完全圖、路、圈、以及直徑為n -2 (n≥10)的樹的3-ASC指標(biāo)。同時證明了直徑為2的圖G的指標(biāo)θ3(G)∈ {3,4}等極值結(jié)論。在第三章中我們研究幾乎邊緣圖的一些構(gòu)造問題,并給出任意圖G的指標(biāo)上界等極值問題。第四章對本論文進行了總結(jié)并列舉了一些論文中還有待進一步解決的問題。
[Abstract]:All the graphs involved in this paper are simple undirected connected graphs. The distance between two vertices u and v of a connected graph dG (uv) is defined as the length of the shortest path between u and v, and the centrifuge eccG (u) of u is the maximum distance between u and all other points in graph G. The center set C (G) and edge set P (G) of connected graph G are composed of vertices with minimum centrifuge rate and maximum centrifuge rate respectively. By C (G) = V (G)-2, the graph G is almost self-centered (almost self-centered graph, ASC graph). If P (G) is V (G)-1, the graph G is almost edge graph (almost-peripheral graph, AP graph). In this paper, we study the extremum problem of almost self center graph and almost edge graph respectively. The first chapter briefly introduces some basic concepts, symbols and related research background of the graphs involved in this paper, and gives the relevant definitions of AS graphs and AP graphs. In chapter 2, we give the 3-ASC indices of complete graphs, paths, cycles and trees with n -2 diameter (n 鈮，

本文編號：2401381