Graph-theoretical versus topological ends of graphs
نویسندگان
چکیده
منابع مشابه
Graph-theoretical versus topological ends of graphs
We compare the notions of an end that exist in the graph-theoretical and, independently, in the topological literature. These notions conflict except for locally finite graphs, and we show how each can be expressed in the context of the other. We find that the topological ends of a graph are precisely the undominated of its graph-theoretical ends, and that graph theoretical ends have a simple t...
متن کاملEnds—group Theoretical and Topological Aspects
This is a survey of topological, group theoretical and some graph theoretical aspects of ends. After discussing the notion of ends in topology, we consider ends of graphs and show that the metric end topology of connected graphs is metrizable. The “1–2–Cantor theorem” is proved for graphs whose ends are all limit ends, that is, ends which are accumulation points of an orbit of the group of auto...
متن کاملSome Graph-Theoretical Aspects of the Golden Ratio: Topological Index, Isomatching Graphs, and Golden Family Graphs
By defining the non-adjacent number, p(G, k), and topological index, ZG, for a graph G, several sequences of graphs are shown to be closely related to the golden ratio, τ. Namely, the Z-values of the path and cycle graphs are Fibonacci, and Lucas numbers, respectively, and thus the ratio of consecutive terms of Z converges to τ. Several new sequences of graphs (golden family graphs) were found ...
متن کاملA graph-theoretical invariant of topological spaces
Given a topological space T and a finite subset T0 of T , we associate two graphs with T and T0 that, under rather mild conditions, turn out to be a block graph and a tree, respectively. This construction is of interest, e.g., in the context of phylogenetic analysis where T may model a full ‘‘orbit’’ of a dynamical branching process, and T0 the set of its branching points. © 2008 Elsevier Ltd. ...
متن کاملOn trivial ends of Cayley graph of groups
In this paper, first we introduce the end of locally finite graphs as an equivalence class of infinite paths in the graph. Then we mention the ends of finitely generated groups using the Cayley graph. It was proved that the number of ends of groups are not depended on the Cayley graph and that the number of ends in the groups is equal to zero, one, two, or infinity. For ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2003
ISSN: 0095-8956
DOI: 10.1016/s0095-8956(02)00034-5