On Distributive Ring and Hereditary Property

2021 ◽  
Author(s):  
Shahad M. Moteea ◽  
Muthana A. Mahmood
Keyword(s):  
Distributive Ring ◽  
Hereditary Property

Minimal Characteristic Algebras for Rectangular k-Normal Identities

2011 ◽  
Vol 18 (04) ◽  
pp. 611-628
Author(s):  
K. Hambrook ◽  
S. L. Wismath
Keyword(s):  
Hereditary Property ◽  
Fixed Type ◽  
Hereditary Properties

A characteristic algebra for a hereditary property of identities of a fixed type τ is an algebra [Formula: see text] such that for any variety V of type τ, we have [Formula: see text] if and only if every identity satisfied by V has the property p. This is equivalent to [Formula: see text] being a generator for the variety determined by all identities of type τ which have property p. Płonka has produced minimal (smallest cardinality) characteristic algebras for a number of hereditary properties, including regularity, normality, uniformity, biregularity, right- and leftmost, outermost, and external-compatibility. In this paper, we use a construction of Płonka to study minimal characteristic algebras for the property of rectangular k-normality. In particular, we construct minimal characteristic algebras of type (2) for k-normality and rectangularity for 1 ≤ k ≤ 3.

scholarly journals Some Features of Intuitionistic L- R1 Spaces

2018 ◽  
Vol 10 (1) ◽  
pp. 1-9
Author(s):  
R. Islam ◽  
M. S. Hossain
Keyword(s):  
Continuous Mapping ◽  
Topological Spaces ◽  
Hereditary Property

In this paper, we have introduced four notions of R1 space in intuitionistic L-topological spaces and established some implications among them. We have also proved that all of these definitions satisfy “good extension” and “hereditary” property. Finally, it has been shown that all concepts are preserved under one-one, onto and continuous mapping.

Research on the Hereditary Properties of the Cartesian Product Operation of Graphs

2012 ◽  
Vol 241-244 ◽  
pp. 2802-2806
Author(s):  
Hua Dong Wang ◽  
Bin Wang ◽  
Yan Zhong Hu
Keyword(s):  
Euler Characteristic ◽  
Cartesian Product ◽  
Hamilton Cycle ◽  
Hereditary Property ◽  
Constant Property ◽  
Product Graph ◽  
Product Operation ◽  
Graph Operation ◽  
Hereditary Properties

This paper defined the hereditary property (or constant property) concerning graph operation, and discussed various forms of the hereditary property under the circumstance of Cartesian product graph operation. The main conclusions include: The non-planarity and Hamiltonicity of graph are hereditary concerning the Cartesian product, but planarity of graph is not, Euler characteristic and non-hamiltonicity of graph are not hereditary as well. Therefore, when we applied this principle into practice, we testified that Hamilton cycle does exist in hypercube.

scholarly journals The structure of almost all graphs in a hereditary property

2011 ◽  
Vol 101 (2) ◽  
pp. 85-110 ◽  
Author(s):  
Noga Alon ◽  
József Balogh ◽  
Béla Bollobás ◽  
Robert Morris
Keyword(s):  
Hereditary Property ◽  
Almost All

scholarly journals On Completely Normal Spaces

2019 ◽  
Vol 24 (5) ◽  
pp. 111
Author(s):  
Taha H. Jasim1 ◽  
Luma H. Othman
Keyword(s):  
Topological Property ◽  
Normal Space ◽  
Hereditary Property ◽  
New Class ◽  
The Subject ◽  
The Relationship

The purpose of this paper is to introduce a new class of completely normal spaces namely , ) completely normal space . The relationship between them was studied and we investigate some characterizations of them. At last we give more of examples to explain the subject and study the topological property and hereditary property of these types.   http://dx.doi.org/10.25130/tjps.24.2019.099

scholarly journals The Edit Distance Function and Symmetrization

10.37236/2262 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
Ryan R. Martin
Keyword(s):  
Distance Function ◽  
Edit Distance ◽  
Symmetric Difference ◽  
Hereditary Property ◽  
Vertex Set ◽  
Hereditary Properties

The edit distance between two graphs on the same labeled vertex set is the size of the symmetric difference of the edge sets.  The distance between a graph, G, and a hereditary property, ℋ, is the minimum of the distance between G and each G'∈ℋ.  The edit distance function of ℋ is a function of p∈[0,1] and is the limit of the maximum normalized distance between a graph of density p and ℋ.This paper utilizes a method due to Sidorenko [Combinatorica 13(1), pp. 109-120], called "symmetrization", for computing the edit distance function of various hereditary properties.  For any graph H, Forb(H) denotes the property of not having an induced copy of H.  This paper gives some results regarding estimation of the function for an arbitrary hereditary property. This paper also gives the edit distance function for Forb(H), where H is a cycle on 9 or fewer vertices.

scholarly journals A Note on the Speed of Hereditary Graph Properties

10.37236/644 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Vadim V. Lozin ◽  
Colin Mayhill ◽  
Victor Zamaraev
Keyword(s):  
Practical Importance ◽  
Bipartite Graphs ◽  
Hereditary Property ◽  
Induced Subgraphs ◽  
Forbidden Induced Subgraphs ◽  
Graph Properties ◽  
Graph Property ◽  
Vertex Set ◽  
Split Graphs ◽  
Hereditary Properties

For a graph property $X$, let $X_n$ be the number of graphs with vertex set $\{1,\ldots,n\}$ having property $X$, also known as the speed of $X$. A property $X$ is called factorial if $X$ is hereditary (i.e. closed under taking induced subgraphs) and $n^{c_1n}\le X_n\le n^{c_2n}$ for some positive constants $c_1$ and $c_2$. Hereditary properties with the speed slower than factorial are surprisingly well structured. The situation with factorial properties is more complicated and less explored, although this family includes many properties of theoretical or practical importance, such as planar graphs or graphs of bounded vertex degree. To simplify the study of factorial properties, we propose the following conjecture: the speed of a hereditary property $X$ is factorial if and only if the fastest of the following three properties is factorial: bipartite graphs in $X$, co-bipartite graphs in $X$ and split graphs in $X$. In this note, we verify the conjecture for hereditary properties defined by forbidden induced subgraphs with at most 4 vertices.

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