Graph-theoretical versus topological ends of graphs
نویسندگان
چکیده
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 topological description generalizing the definition of a topological end.
منابع مشابه
Ends—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 کاملUse of Structure Codes (Counts) for Computing Topological Indices of Carbon Nanotubes: Sadhana (Sd) Index of Phenylenes and its Hexagonal Squeezes
Structural codes vis-a-vis structural counts, like polynomials of a molecular graph, are important in computing graph-theoretical descriptors which are commonly known as topological indices. These indices are most important for characterizing carbon nanotubes (CNTs). In this paper we have computed Sadhana index (Sd) for phenylenes and their hexagonal squeezes using structural codes (counts). Sa...
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 کاملOn computing the general Narumi-Katayama index of some graphs
The Narumi-Katayama index was the first topological index defined by the product of some graph theoretical quantities. Let $G$ be a simple graph with vertex set $V = {v_1,ldots, v_n }$ and $d(v)$ be the degree of vertex $v$ in the graph $G$. The Narumi-Katayama index is defined as $NK(G) = prod_{vin V}d(v)$. In this paper, the Narumi-Katayama index is generalized using a $n$-ve...
متن کاملThe topological ordering of covering nodes
The topological ordering algorithm sorts nodes of a directed graph such that the order of the tail of each arc is lower than the order of its head. In this paper, we introduce the notion of covering between nodes of a directed graph. Then, we apply the topological orderingalgorithm on graphs containing the covering nodes. We show that there exists a cut set withforward arcs in these...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 87 شماره
صفحات -
تاریخ انتشار 2003