منابع مشابه
The Path Space of a Directed Graph
We construct a locally compact Hausdorff topology on the path space of a directed graph E and identify its boundary-path space ∂E as the spectrum of a commutative C∗-subalgebra DE of C∗(E). We then show that ∂E is homeomorphic to a subset of the infinite-path space of any desingularisation F of E. Drinen and Tomforde showed that we can realise C∗(E) as a full corner of C∗(F ), and we deduce tha...
متن کاملDirected prime graph of non-commutative ring
Prime graph of a ring R is a graph whose vertex set is the whole set R any any two elements $x$ and $y$ of $R$ are adjacent in the graph if and only if $xRy = 0$ or $yRx = 0$. Prime graph of a ring is denoted by $PG(R)$. Directed prime graphs for non-commutative rings and connectivity in the graph are studied in the present paper. The diameter and girth of this graph are also studied in the pa...
متن کاملThe path space of a higher-rank graph
We construct a locally compact Hausdorff topology on the path space of a finitely aligned k -graph Λ . We identify the boundary-path space ∂Λ as the spectrum of a commutative C ∗ -subalgebra D Λ of C ∗ (Λ) . Then, using a construction similar to that of Farthing, we construct a finitely aligned k -graph Λ ̃ with no sources in which Λ is embedded, and show that ∂Λ is homeomorphic to a subset of ...
متن کاملSpecial asteroidal quadruple on directed path graph non rooted path graph
An asteroidal triple in a graph G is a set of three nonadjacent vertices such that for any two of them there exists a path between them that does not intersect the neighborhood of the third. Special asteroidal triple in a graph G is an asteroidal triple such that each pair is linked by a special connection. A special asteroidal triples play a central role in a characterization of directed path ...
متن کاملOn the Space Complexity of Directed Graph Reachability
Graph reachability problems are fundamental to the study of complexity classes. It is well known that the reachability problem for general directed graphs is known to be complete for non-deterministic logspace (NL). Various restrictions of graph reach-ability are known to capture low level complexity classes. Recently, in a breakthrough result, it was shown that reachability problem for undirec...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2013
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2013-11755-7