scholarly journals Weak integer additive set-labeled graphs: A creative review

2015 ◽  
Vol 08 (03) ◽  
pp. 1550052 ◽  
Author(s):  
N. K. Sudev ◽  
K. A. Germina ◽  
K. P. Chithra
Keyword(s):  
Binary Operation ◽  
Labeled Graphs ◽  
Injective Function ◽  
Power Set

For a non-empty ground set [Formula: see text], finite or infinite, the set-valuation or set-labeling of a given graph [Formula: see text] is an injective function [Formula: see text], where [Formula: see text] is the power set of the set [Formula: see text]. A set-valuation or a set-labeling of a graph [Formula: see text] is an injective set-valued function [Formula: see text] such that the induced function [Formula: see text] is defined by [Formula: see text] for every [Formula: see text], where [Formula: see text] is a binary operation on sets. Let [Formula: see text] be the set of all non-negative integers and [Formula: see text] be its power set. An integer additive set-labeling (IASL) is defined as an injective function [Formula: see text] such that the induced function [Formula: see text] is defined by [Formula: see text]. An IASL [Formula: see text] is said to be an integer additive set-indexer if [Formula: see text] is also injective. A weak IASL is an IASL [Formula: see text] such that [Formula: see text]. In this paper, critical and creative review of certain studies made on the concepts and properties of weak integer additive set-valued graphs is intended.

A characterization for topologically integer additive set-indexer of graphs

2016 ◽  
Vol 08 (01) ◽  
pp. 1650012
Author(s):  
Seema Mehra ◽  
Puneet
Keyword(s):  
Minimum Cardinality ◽  
Injective Function ◽  
Power Set

The aim of this paper is to introduce a new function that satisfies the property of topological integer additive set-indexer (Top-IASI) with minimum cardinality for pan, tadpole, path and shovel graphs. Let [Formula: see text] be a graph and [Formula: see text] is a nonempty set. If an injective function [Formula: see text] induced a new injective function [Formula: see text] defined by [Formula: see text] for every [Formula: see text] then [Formula: see text] is called set-indexer. If an injective function [Formula: see text] produced another injective function [Formula: see text] defined by [Formula: see text] for every [Formula: see text], where [Formula: see text] is the set of all non-negative integers and [Formula: see text] is its power set then [Formula: see text] is called an integer additive set-indexer (IASI). An IASI is called a Top-IASI if [Formula: see text] forms a topology.

scholarly journals The sparing number of certain graph powers

2019 ◽  
Vol 11 (1) ◽  
pp. 186-202 ◽  
Author(s):  
N. K. Sudev ◽  
K. P. Chithra ◽  
K. A. Germina
Keyword(s):  
Injective Function ◽  
Power Set ◽  
Minimum Number

Abstract Let ℕ0 be the set of all non-negative integers and 𝒫(ℕ0) be its power set. Then, an integer additive set-indexer (IASI) of a given graph G is an injective function f : V(G) → P(ℕ0) such that the induced function f+ : E(G) → 𝒫(ℕ0) defined by f+(uv) = f(u) + f(v) is also injective. An IASI f is said to be a weak IASI if |f+(uv)| = max(|f(u)|, |f(v)|) for all u, v ∈ V(G). A graph which admits a weak IASI may be called a weak IASI graph. The set-indexing number of an element of a graph G, a vertex or an edge, is the cardinality of its set-labels. The sparing number of a graph G is the minimum number of edges with singleton set-labels, required for a graph G to admit a weak IASI. In this paper, we study the admissibility of weak IASI by certain graph powers and their corresponding sparing numbers.

scholarly journals On certain arithmetic integer additive set-indexers of graphs

2015 ◽  
Vol 07 (03) ◽  
pp. 1550025 ◽  
Author(s):  
N. K. Sudev ◽  
K. A. Germina
Keyword(s):  
Arithmetic Progressions ◽  
Injective Function ◽  
Power Set

Let ℕ0 denote the set of all non-negative integers and 𝒫(ℕ0) be its power set. An integer additive set-indexer (IASI) of a graph G is an injective function f : V(G) → 𝒫(ℕ0) such that the induced function f+ : E(G) → 𝒫(ℕ0) defined by f+ (uv) = f(u) + f(v) is also injective. A graph G which admits an IASI is called an integer additive set-indexed graph (IASI-graph). An IASI of a graph G is said to be an arithmetic IASI if the elements of the set-labels of all vertices and edges of G are in arithmetic progressions. In this paper, we discuss about two special types of arithmetic IASIs.

scholarly journals A study on the modular sumset labeling of graphs

2017 ◽  
Vol 09 (03) ◽  
pp. 1750039 ◽  
Author(s):  
Sudev Naduvath
Keyword(s):  
Positive Integer ◽  
Injective Function ◽  
Power Set

For a positive integer [Formula: see text], let [Formula: see text] be the set of all non-negative integers modulo [Formula: see text] and [Formula: see text] be its power set. A modular sumset valuation or a modular sumset labeling of a given graph [Formula: see text] is an injective function [Formula: see text] such that the induced function [Formula: see text] defined by [Formula: see text]. A modular sumset indexer of a graph [Formula: see text] is an injective modular sumset valued function [Formula: see text] such that the induced function [Formula: see text] is also injective. In this paper, some properties and characteristics of this type of modular sumset labeling of graphs are being studied.

Migration and family change in Egypt: a comparative approach to social remittances

2013 ◽  
Vol 10 (1) ◽  
pp. 71-80 ◽  
Author(s):  
Lucile Gruntz ◽  
Delphine Pagès-El Karoui
Keyword(s):  
Public Discourse ◽  
Comparative Approach ◽  
Structural Factors ◽  
Host Countries ◽  
Return Policies ◽  
Social Remittances ◽  
Power Set ◽  
Gender Ideals ◽  
Gulf States ◽  
And Gender

Based on two ethnographical studies, our article explores social remittances from France and from the Gulf States, i.e. the way Egyptian migrants and returnees contribute to social change in their homeland with a focus on gender ideals and practices, as well as on the ways families cope with departure, absence and return. Policies in the home and host countries, public discourse, translocal networks, and individual locations within evolving structures of power, set the frame for an analysis of the consequences of migration in Egypt. This combination of structural factors is necessary to grasp the complex negotiations of family and gender norms, as asserted through idealized models, or enacted in daily practices in immigration and back home.

Using binary operations to construct a transitive set of block transformations

2020 ◽  
Vol 30 (6) ◽  
pp. 375-389
Author(s):  
Igor V. Cherednik
Keyword(s):  
Binary Operation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Binary Operations ◽  
The Family ◽  
Transitive Set ◽  
Necessary And Sufficient

AbstractWe study the set of transformations {ΣF : F∈ 𝓑∗(Ω)} implemented by a network Σ with a single binary operation F, where 𝓑∗(Ω) is the set of all binary operations on Ω that are invertible as function of the second variable. We state a criterion of bijectivity of all transformations from the family {ΣF : F∈ 𝓑∗(Ω)} in terms of the structure of the network Σ, identify necessary and sufficient conditions of transitivity of the set of transformations {ΣF : F∈ 𝓑∗(Ω)}, and propose an efficient way of verifying these conditions. We also describe an algorithm for construction of networks Σ with transitive sets of transformations {ΣF : F∈ 𝓑∗(Ω)}.

scholarly journals Online Learning Algorithms for the Real-Time Set-Point Tracking Problem

2021 ◽  
Vol 11 (14) ◽  
pp. 6620
Author(s):  
Arman Alahyari ◽  
David Pozo ◽  
Meisam Farrokhifar
Keyword(s):  
Decision Making ◽  
Power Systems ◽  
Real Time ◽  
Demand Response ◽  
Tracking Problem ◽  
Smart Meters ◽  
Set Point ◽  
Point Tracking ◽  
Power Set ◽  
Decision Making Framework

With the recent advent of technology within the smart grid, many conventional concepts of power systems have undergone drastic changes. Owing to technological developments, even small customers can monitor their energy consumption and schedule household applications with the utilization of smart meters and mobile devices. In this paper, we address the power set-point tracking problem for an aggregator that participates in a real-time ancillary program. Fast communication of data and control signal is possible, and the end-user side can exploit the provided signals through demand response programs benefiting both customers and the power grid. However, the existing optimization approaches rely on heavy computation and future parameter predictions, making them ineffective regarding real-time decision-making. As an alternative to the fixed control rules and offline optimization models, we propose the use of an online optimization decision-making framework for the power set-point tracking problem. For the introduced decision-making framework, two types of online algorithms are investigated with and without projections. The former is based on the standard online gradient descent (OGD) algorithm, while the latter is based on the Online Frank–Wolfe (OFW) algorithm. The results demonstrated that both algorithms could achieve sub-linear regret where the OGD approach reached approximately 2.4-times lower average losses. However, the OFW-based demand response algorithm performed up to twenty-nine percent faster when the number of loads increased for each round of optimization.

scholarly journals k-Zumkeller labeling of super subdivision of some graphs

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
M. Basher
Keyword(s):  
Simple Graph ◽  
Natural Numbers ◽  
Injective Function ◽  
Planar Grid ◽  
Circular Ladder

AbstractA simple graph $$G=(V,E)$$ G = ( V , E ) is said to be k-Zumkeller graph if there is an injective function f from the vertices of G to the natural numbers N such that when each edge $$xy\in E$$ x y ∈ E is assigned the label f(x)f(y), the resulting edge labels are k distinct Zumkeller numbers. In this paper, we show that the super subdivision of path, cycle, comb, ladder, crown, circular ladder, planar grid and prism are k-Zumkeller graphs.

scholarly journals M-Hazy Vector Spaces over M-Hazy Field

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1118
Author(s):  
Faisal Mehmood ◽  
Fu-Gui Shi
Keyword(s):  
Vector Space ◽  
Linear Transformation ◽  
Binary Operation ◽  
Vector Spaces ◽  
Fundamental Properties ◽  
Classical Algebra ◽  
Important Development ◽  
Fuzzy Algebra ◽  
Convex Spaces

The generalization of binary operation in the classical algebra to fuzzy binary operation is an important development in the field of fuzzy algebra. The paper proposes a new generalization of vector spaces over field, which is called M-hazy vector spaces over M-hazy field. Some fundamental properties of M-hazy field, M-hazy vector spaces, and M-hazy subspaces are studied, and some important results are also proved. Furthermore, the linear transformation of M-hazy vector spaces is studied and their important results are also proved. Finally, it is shown that M-fuzzifying convex spaces are induced by an M-hazy subspace of M-hazy vector space.

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