- Algebras of Labelled Graphs

C∗-algebras of Labelled Graphs

We describe a class of C∗-algebras which simultaneously generalise the ultragraph algebras of Tomforde and the shift space C∗-algebras of Matsumoto. In doing so we shed some new light on the different C∗-algebras that may be associated to a shift space. Finally, we show how to associate a simple C∗-algebra to an irreducible sofic shift. keywords: C∗-algebras, labelled graph, ultragraph, Matsumo...

3-difference cordial labeling of some cycle related graphs

Let G be a (p, q) graph. Let k be an integer with 2 ≤ k ≤ p and f from V (G) to the set {1, 2, . . . , k} be a map. For each edge uv, assign the label |f(u) − f(v)|. The function f is called a k-difference cordial labeling of G if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively den...

NILPOTENT GRAPHS OF MATRIX ALGEBRAS

Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...

On Isomorphism of Simplicial Complexes and Their Related Algebras

Generic Commutative Separable Algebras and Cospans of Graphs

We show that the generic symmetric monoidal category with a commutative separable algebra which has a Σ-family of actions is the category of cospans of finite Σ-labelled graphs restricted to finite sets as objects, thus providing a syntax for automata on the alphabet Σ. We use this result to produce semantic functors for Σautomata.