The Graph of Multiplication is Equivalent to Counting
نویسنده
چکیده
Counting is AC -reducible to the graph of multiplication. Hence the graph of multiplication is equivalent under AC reductions to majority and to the function form of multiplication.
منابع مشابه
The small intersection graph relative to multiplication modules
Let $R$ be a commutative ring and let $M$ be an $R$-module. We define the small intersection graph $G(M)$ of $M$ with all non-small proper submodules of $M$ as vertices and two distinct vertices $N, K$ are adjacent if and only if $Ncap K$ is a non-small submodule of $M$. In this article, we investigate the interplay between the graph-theoretic properties of $G(M)$ and algebraic properties of $M...
متن کاملAnalysis of Resting-State fMRI Topological Graph Theory Properties in Methamphetamine Drug Users Applying Box-Counting Fractal Dimension
Introduction: Graph theoretical analysis of functional Magnetic Resonance Imaging (fMRI) data has provided new measures of mapping human brain in vivo. Of all methods to measure the functional connectivity between regions, Linear Correlation (LC) calculation of activity time series of the brain regions as a linear measure is considered the most ubiquitous one. The strength of the dependence obl...
متن کاملPlanarity of Intersection Graph of submodules of a Module
Let $R$ be a commutative ring with identity and $M$ be an unitary $R$-module. The intersection graph of an $R$-module $M$, denoted by $Gamma(M)$, is a simple graph whose vertices are all non-trivial submodules of $M$ and two distinct vertices $N_1$ and $N_2$ are adjacent if and only if $N_1cap N_2neq 0$. In this article, we investigate the concept of a planar intersection graph and maximal subm...
متن کاملAn Optimal Lower Bound on the Number of Variables for Graph Identi cation
In this paper we show that (n) variables are needed for rst-order logic with counting to identify graphs on n vertices. The k-variable language with counting is equivalent to the (k ? 1)-dimensional Weisfeiler-Lehman method. We thus settle a long-standing open problem. Previously it was an open question whether or not 4 variables suuce. Our lower bound remains true over a set of graphs of color...
متن کاملOn Counting Polynomials of Some Nanostructures
The Omega polynomial(x) was recently proposed by Diudea, based on the length of strips in given graph G. The Sadhana polynomial has been defined to evaluate the Sadhana index of a molecular graph. The PI polynomial is another molecular descriptor. In this paper we compute these three polynomials for some infinite classes of nanostructures.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Inf. Process. Lett.
دوره 41 شماره
صفحات -
تاریخ انتشار 1992