Related papers: Separating a chart

For a graph $G = (V, E)$, the $\gamma$-graph of $G$ is the graph whose vertex set is the collection of minimum dominating sets, or $\gamma$-sets of $G$, and two $\gamma$-sets are adjacent if they differ by a single vertex and the two…

Let $\Gamma$ be a discrete group. We show that if $\Gamma$ is nonamenable, then the algebraic tensor products $C^*_r(\Gamma)\otimes C^*_r(\Gamma)$ and $C^*(\Gamma)\otimes C^*_r(\Gamma)$ do not admit unique $C^*$-norms. Moreover, when…

We introduce the notion of the action of a group on a labeled graph and the quotient object, also a labeled graph. We define a skew product labeled graph and use it to prove a version of the Gross-Tucker theorem for labeled graphs. We then…

Let $\Gamma$ be a $G$-symmetric graph with vertex set $V$. We suppose that $V$ admits a $G$-partition $\mathcal{B} = \{ B_0, ... , B_b \}$, with parts of size $v$, and that the quotient graph induced on $\mathcal B$ is a complete graph of…

We introduce a generalisation of Condition (K) to finitely separated graphs and show that it is equivalent to essential freeness of the associated partial action as well as the exchange property of any of the associated tame algebras. As a…

Let $\xi:C^*(E)\to C^*(F)$ be a unital $*$-homomorphism between simple purely infinite Cuntz-Krieger algebras of finite graphs. We prove that there exists a unital $*$-homomorphism $\phi:L(E)\to L(F)$ between the corresponding Leavitt…

The disk graph of a handlebody H of genus g at least 2 with m marked points on the boundary is the graph whose vertices are isotopy classes of disks disjoint from the marked points and where two vertices are connected by an edge if they can…

We provide a matrix-based formula for the Tutte symmetric function of a graph. In particular, for any graph $G$ with a designated head and tail vertex, we describe an infinite matrix $M_G$ from which the Tutte symmetric function can be…

We construct a $C^1$ symplectic twist map $g$ of the annulus that has an essential invariant curve $\Gamma$ such that $\Gamma$ is not differentiable and $g$ restricted to $\Gamma$ is minimal.

Let $\Gamma$ be a finite, undirected, connected, simple graph. We say that a matching $\mathcal{M}$ is a \textit{permutable $m$-matching} if $\mathcal{M}$ contains $m$ edges and the subgroup of $\text{Aut}(\Gamma)$ that fixes the matching…

Given a directed graph $E$ and a labeling $\mathcal{L}$, one forms the labeled graph $C^*$-algebra by taking a weakly left--resolving labeled space $(E, \mathcal{L}, \mathcal{B})$ and considering a universal generating family of partial…

The graph C*-algebra of a directed graph E is the universal C*-algebra generated by a family of partial isometries satisfying relations which reflect the path structure of E. In the first part of this paper we consider coverings of directed…

We geometrically describe the relation induced on a set of graphs by isomorphism of their associated graph C*-algebras as the smallest equivalence relation generated by five types of moves. The graphs studied have finitely many vertices and…

By a labeled graph $C^*$-algebra we mean a $C^*$-algebra associated to a labeled space $(E,\mathcal L,\mathcal E)$ consisting of a labeled graph $(E,\mathcal L)$ and the smallest normal accommodating set $\mathcal E$ of vertex subsets.…

We study how the number $c(X)$ of components of a graph $X$ can be expressed through the number and properties of the components of a quotient graph $X/\sim.$ We partially rely on classic qualifications of graph homomorphisms such as…

In this paper, we investigate certain graphs defined on groups, with a focus on infinite groups. The graphs discussed are the power graph, the enhanced power graph, and the commuting graph whose vertex set is a group $G$. The power graph is…

Let $E$ and $F$ be two Hilbert $C^*$-modules over $C^*$-algebras $A$ and $B$, respectively. Let $T$ be a surjective linear isometry from $E$ onto $F$ and $\varphi$ a map from $A$ into $B$. We will prove in this paper that if the…

This paper compares the divisorial gonality of a finite graph $G$ to the divisorial gonality of the associated metric graph $\Gamma(G,\mathbb{1})$ with unit lengths. We show that $\text{dgon}(\Gamma(G,\mathbb{1}))$ is equal to the minimal…

We introduce uniformly vertex-transitive graphs as vertex-transitive graphs satisfying a stronger condition on their automorphism groups, motivated by a problem which arises from a Sinkhorn-type algorithm. We use the derangement graph…

We prove that ample groupoids with sigma-compact unit spaces are equivalent if and only if they are stably isomorphic in an appropriate sense, and relate this to Matui's notion of Kakutani equivalence. We use this result to show that…