Related papers: Characterizing Liminal And Type I Graph C*-Algebra…

Given a finite set T of maps on a finite ring R, we look at the finite simple graph G=(V,E) with vertex set V=R and edge set E={(a,b) | exists t in T, b=t(a), b not equal to a}. An example is when R=Z_n and T consists of a finite set of…

Inspired by Franks' classification of irreducible shifts of finite type we provide a short list of allowed moves on graphs that preserves the stable isomorphism class of the associated C*-algebras. We show that if two graphs have stably…

We give a concrete formula for the unique faithful trace on the finite simple non-AF labeled graph $C^*$-algebra $C^*(E_{\mathbb{Z}}, \mathcal{L}, \overline{\mathcal{E}}_{\mathbb{Z}})$ associated to the Thue--Morse sequence…

The notion of ends in an infinite graph $G$ might be modified if we consider them as equivalence classes of infinitely edge-connected rays, rather than equivalence classes of infinitely (vertex-)connected ones. This alternative definition…

We characterise quasidiagonality of the $C^*$-algebra of a cofinal $k$-graph in terms of an algebraic condition involving the coordinate matrices of the graph. This result covers all simple $k$-graph $C^*$-algebras. In the special case of…

A graph $G$ is {\it $n$-existentially closed} if, for all disjoint sets of vertices $A$ and $B$ with $|A\cup B|=n$, there is a vertex $z$ not in $A\cup B$ adjacent to each vertex of $A$ and to no vertex of $B$. In this paper, we investigate…

We define an admissible decomposition of a graph $E$ into subgraphs $F_1$ and $F_2$, and consider the intersection graph $F_1\cap F_2$ as a subgraph of both $F_1$ and $F_2$. We prove that, if the graph $E$ is row finite and its…

We explicitly describe two-sided ideals in Leavitt path algebras associated with a row-finite graph. Our main result is that any two-sided ideal $I$ of a Leavitt path algebra associated with a row-finite graph is generated by elements of…

For any countable directed graph E we describe the primitive ideal space of the corresponding generalized Cuntz-Krieger algebra C*(E).

Given a finitely aligned $k$-graph $\Lambda$, we let $\Lambda^i$ denote the $(k-1)$-graph formed by removing all edges of degree $e_i$ from $\Lambda$. We show that the Toeplitz-Cuntz-Krieger algebra of $\Lambda$, denoted by…

We prove that if E and F are graphs with a finite number of vertices and an infinite number of edges, if K is a field, and if L_K(E) and L_K(F) are simple Leavitt path algebras, then L_K(E) is Morita equivalent to L_K(F) if and only if…

We study the class of simple graphs $\mathcal{G}^*$ for which every pair of distinct odd cycles intersect in at most one edge. We give a structural characterization of the graphs in $\mathcal{G}^*$ and prove that every $G \in \mathcal{G}^*$…

An old result of M\"uller and R\"odl states that a countable graph $G$ has a subgraph whose vertices all have infinite degree if and only if for any vertex labeling of $G$ by positive integers, an infinite increasing path can be found. They…

We consider directed graphs E which have been obtained by adding a sink to a fixed graph G. We associate an element of Ext(C*(G)) to each such E, and show that the classes of two such graphs are equal in Ext(C*(G)) if and only if the…

We investigate the structure of connected graphs, not necessarily locally finite, with infinitely many ends. On the one hand we study end-transitive such graphs and on the other hand we study such graphs with the property that the…

A $k$-regular graph of girth $g$ is called edge-girth-regular graph, shortly egr-graph, if each of its edges is contained in exactly $\lambda$ distinct $g-$cycles. An egr-graph is called extremal for the triple $(k, g, \lambda)$ if has the…

It is shown that for a given infinite graph $G$ on countably many vertices, and a compact, infinite set of real numbers $\Lambda$ there is a real symmetric matrix $A$ whose graph is $G$ and its spectrum is $\Lambda$. Moreover, the set of…

The results obtained in this paper grew from an attempt to generalize the main theorem of [1]. There it was shown that any circuit injection (a 1-1 onto edge map f such that if C is a circuit then f(C) is a circuit) from a 3-connected, not…

We investigate the ascending Loewy socle series of Leavitt path algebras $L_K(E)$ for an arbitrary graph $E$ and field $K$. We classify those graphs $E$ for which $L_K(E)=S_{\lambda}$ for some element $S_{\lambda}$ of the Loewy socle…

By a finite type-graph we mean a graph whose set of vertices is the set of all $k$-subsets of $[n]=\{1,2,\ldots, n\}$ for some integers $n\ge k\ge 1$, and in which two such sets are adjacent if and only if they realise a certain order type…