Let ? be some context-free graph. We give suucient conditions on a semi-group of bisimulations H ensuring that the quotient Hn? is context-free. Using these suucient conditions we show that the quotient Aut(?)n? of ? by its full group of automorphisms is always context-free. We then give examples showing optimality (in some sense) of the above result.

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 ar...

We prove a certain polynomial congruence modulo an odd prime p ≥ 5, and as a consequence we obtain a congruence for the cube of the Fermat quotient to base 2 in terms of simple finite sums. This extends known results of a similar nature for the first and second powers of the Fermat quotient.

We show there is an uncountable number of parallel total perfect codes in the integer lattice graph Λ of R. In contrast, there is just one 1-perfect code in Λ and one total perfect code in Λ restricting to total perfect codes of rectangular grid graphs (yielding an asymmetric, Penrose, tiling of the plane). We characterize all cycle products Cm × Cn with parallel total perfect codes, and the d-...

We present the main results on 2PFA’s and on the Hadamard quotient of formal power series, the connection between the two notions being a result stating that the event defined by a 2PFA is the Hadamard quotient of two rational power series.

We show that, for an arbitrary graph, a regular ideal of the associated Leavitt path algebra is also graded. As consequence, row-finite we obtain that quotient by again and Condition (L) preserved quotients ideals. Furthermore, describe vertex set make comparison between theory ideals in algebras graph C*-algebras.

We classify those manifolds mentioned in the title which have finite topological type. Namely we show any such connected M is isomorphic to a hyperkähler quotient of a flat quaternionic vector space H by an abelian group. We also show that a compact connected and simply connected 3-Sasakian manifold of dimension 4n− 1 whose isometry group has rank n+1 is isometric to a 3-Sasakian quotient of a ...

For any $k in mathbb{N}$, the $k$-subdivision of graph $G$ is a simple graph $G^{frac{1}{k}}$, which is constructed by replacing each edge of $G$ with a path of length $k$. In [Moharram N. Iradmusa, On colorings of graph fractional powers, Discrete Math., (310) 2010, No. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $G$ has been introduced as a fractional power of $G$, denoted by ...

Soft set is a classification of elements the universe with respect to some given parameters. It new approach for modeling vagueness and uncertainty. The concept soft graph used provide parameterized point view graphs. In this paper we introduce concepts subdivision graph, power line investigate their properties.

We show that the zeta function of a regular graph admits a representation as a quotient of a determinant over a L 2-determinant of the combinatorial Laplacian.