Total Domination Research Articles

Upper Total Domination in Claw-Free Cubic Graphs

Upper Total Domination in Claw-Free Cubic Graphs

Minimum Randić Index of Trees with Fixed Total Domination Number

The Randić index is among the most famous degree-based topological indices in chemical graph theory. It was introduced due to its application in modeling the properties of certain molecular structures and has been extensively studied. In this paper, we study the lower bound of the Randić index of trees in terms of the order and the total domination number. Finally, trees with the minimal Randić index are characterized.

Dragonfly Algorithm-Based Optimization for Selective Harmonics Elimination in Cascaded H-Bridge Multilevel Inverters with Statistical Comparison

Harmonics worsen the quality of electrical signals, hence, there is a need to eliminate them. The test objects under discussion are single-phase versions of cascaded H-bridge (CHB) multilevel inverters (MLIs) whose switching angles are optimized to eliminate specific harmonics. The Dragonfly Algorithm (DA) is used to eradicate low-order harmonics, and its statistical performance is compared to that of many other optimization techniques, including Particle Swarm Optimization (PSO), Accelerated Particle Swarm Optimization (APSO), Differential Evolution (DE), and Grey Wolf Optimization (GWO). Various scenarios of the algorithms’ search agent population for inverters with seven, nine, and eleven levels of output voltages are comprehensively addressed in this research. No algorithm shows total dominance in every scenario. The DA is least impacted by the change in dimensions of the narrated problem.

Domination type parameters of Pell graphs

Pell graphs are defined on certain ternary strings as special subgraphs of Fibonacci cubes of odd index. In this work the domination number, total domination number, 2-packing number, connected domination number, paired domination number, and signed domination number of Pell graphs are studied. Using integer linear programming, exact values and some estimates for these numbers of small Pell graphs are obtained. Furthermore, some theoretical bounds are obtained for the domination numbers and total domination numbers of Pell graphs.

Total mixed domination in graphs

For a graph we call a subset a total mixed dominating set of G if each element of is either adjacent or incident to an element of S, and the total mixed domination number of G is the minimum cardinality of a total mixed dominating set of G. In this paper, we initiate to study the total mixed domination number of a connected graph by giving some tight bounds in terms of some parameters such as order and total domination numbers of the graph and its line graph. Then we discuss on the relation between total mixed domination number of a graph and its diameter. Study of this number in trees and 2-corona graphs is our next work. Also we show that the total mixed domination number of a graph is equal to the total domination number of its total graph. Giving the total mixed domination numbers of the paths, cycles, complete bipartite graphs, complete graphs and wheels is our last work.

On the Forcing Domination and the Forcing Total Domination Numbers of a Graph

On the Forcing Domination and the Forcing Total Domination Numbers of a Graph

Some Properties of Von Neumann Regular Graphs of Rings

Let R be a ring with unity. Taloukolaei and Sahebi [2] introduced the Von Neumann regular graph GV nr+(R) of a ring, whose vertex set is R and two distinct vertices x and y are adjacent if and only if x + y is a Von Neumann regular element. In this article, we investigate some new properties of GV nr+(R) such as traversability, pancyclic, unicyclic, chordal and perfect. We also investigate the domination parameters of GV nr+(R) such as dominating set, domination number, total domination number, connected domination number and give the condition when the GV nr+(R) is an excellent graph. Finally we determine the bondage number.

Analysis of Vulnerability of Some Transformation Networks

In several different applications and contexts, networks are essential frameworks and appear.Vulnerability value is a measure of the network’s durability in the face of damage that may lead to a reduction or complete loss of the network’s particular functionality. The domination number and it’s types can be used network vulnerability parameters. Recently, the disjunctive total domination number has been defined by Henning and Naicker. In this paper, the disjunctive total domination numbers of the transformation graph [Formula: see text] when [Formula: see text] of some graphs [Formula: see text] have been obtained. Furthermore, some new general results have been given for the parameter mentioned above.

The Domination Parameters on a kind of the regular honeycomb structure

The honeycomb mesh, based on hexagonal structure, has enormous applications in chemistry and engineering. A major challenge in this field is to understand the unique properties of honeycomb structures, which depend on their properties of topology. One of the important concepts in graph theory is the domination number which can be used for network control and monitoring. In this paper, we investigate the domination number of the honeycomb network. For this purpose, the domination number, the total domination number, the independent domination number, the connected domination number and the doubly connected domination number of the honeycomb are obtained. Finally, in some honeycomb structures of real models, we obtain the exact amount of these parameters.

Hinge Total Domination on Some Graph Families

set S of vertices in a graph G = (V (G);E(G)) is a hinge dominating set if every vertex \(u\) \(\in\) V \(\setminus \) \(S\) is adjacent to some vertex \(u\) \(\in\) \(S\) and a vertex \(w\) \(\in\) V \(\setminus\) \(S\) such that (\(v\), \(w\)) is not an edge in E(G). The hinge domination number \(\gamma\)\(h\)(\(G\)) is the minimum size of a hinged dominating set. A set S is called a total dominating set of G if for every vertex in V , including those in S is adjacent to at least one vertex in S. The cardinality of a minimum total dominating set in G is called the total domination number of G and denoted as \(\gamma\)\(h\)(\(G\)) In this study, a new parameter called hinged total dominating set was introduced and defined as, a hinge total dominating set of a graph G is a set S of vertices of G such that S is both a hinge dominating set and total dominating set. The hinge total domination number, \(\gamma\)\(h\)(\(G\)) is the minimum cardinality of a hinge total dominating set of G. We initiate a study of hinge total dominating set and present its characterization. In addition, we also determine the exact values of hinge total domination number on some graph families.

Кey trends in the financial services digital transformation in Russia and their influence on consumer experience: forecast of expertsm

Purpose: forecasting the key avenues for financial services digital transformation in Russia and its influence on customer experience based on expert surveys.Methods: a set of general scientific methods of analysis and synthesis, as well as marketing research methods – desk and field research. The field research included qualitative method: in-depth interviews with financial market experts. The obtained data were analyzed using content analysis and summarized. Results: the authors provided analysis of secondary data on the main global and local digitalization trends in the financial services market and conducted analytical aggregation of expert opinions on the most likely future changes in the financial services market in the process of digitalization. Analysis of the obtained data enabled to describe three avenues for financial services digital transformation – means of payments digital transformation, payments infrastructure digital transformation and customer interaction models digital transformation. The authors also presented and described the positive and negative influence of the results of digital transformation on the consumer experience.Conclusions and Relevance: the results of this study emphasize the role of financial services digital transformation in the process of new consumer experience creation. The means of payments digital transformation will ensure the total dominance of digital money within the money circulation system positively affecting consumer experience in terms of growing convenience, speed and cost-cutting. Payment infrastructure digital transformation will positively influence on consumer experience by simplifying the customer identification systems and reducing errors. Customer interaction models digital transformation will enhance the level of seamlessness leading to the full integration of financial services in the day-to-day customer activities. The results of the study can be used to develop strategies enabling to achieve the highest level of competitiveness for the financial service providers in the market.

The PLO’s political communication arena; Arafat and the struggle for media legitimacy

ABSTRACT The Palestine Liberation Organization has been extensively studied and researched in a variety of disciplines and perspectives. However, little attention has been paid to its media and/or political communication strategies that went hand in hand with its political evolution and aims from 1969 to 1982, a period marked by flux and political uncertainty as well intensive PLO state-building processes. This paper seeks to partially fill the gap by addressing political communication not only as a fundamental political practice and strategy but also as an arena in which political elites compete to achieve media legitimacy and ensure support for their objectives and ideologies. Drawing on archival research of the PLO mass media platforms during the period under review, primary sources and interviews with former PLO media personnel, the paper begins with an overview of the PLO’s investment in mass media institutions and other cultural genres before discussing its political communication strategy and its aims in the period from 1969 to 1982. The paper then addresses how the late PLO chairman Yasser Arafat actively competed in the political communication arena to achieve media legitimacy and secure public consent for the PLO’s ideologies and aims. In doing so, the paper does not suggest Arafat achieved total domination of the political communication space nor that other guerrilla leaders, Arab and other actors did not compete in this arena. Rather, the approach emphasizes the relationship between political agency and structure during moments of flux and change, thus complementing dominant approaches in political communication research that focus on framing and discourse.

Being Earth: The Culture of Nature in a Post-Holocene World

How do we gain a sane footing on a planet we’ve spent thousands of years as a geophysical bully wielding ever more clever tools and powerful machines in a mad quest for total domination?

BILANGAN INVERS DOMINASI TOTAL PADA GRAF BUNGA DAN GRAF TRAMPOLIN

Given a simple, finite, undirected and contains no isolated vertices graph , with is the set of vertices in and is the set of edges in . The set is called the dominating set in if for every vertex of is adjacent to at least one vertex in . The set is called the total dominating set in graph if for every vertex in is adjacent to at least one vertices in . If is the total domination set with minimum cardinality of the graph and contains another total domination set, for example , then is called the inverse set of total domination respect to . The minimum cardinality of an inverse set of total domination is called the inverse of total domination number which is denoted by .The set of domination and total domination is not singular. A graph that has a total domination set does not necessarily have a inverse total domination set. In this study, exact values are found of , and and,, n is even and , where be a flower graph and T<span style='font-size:10.0pt;mso-ansi-font-siz

Bilangan Invers Dominasi Total Pada Triangular Snake Graph, Line Triangular Snake Graph, dan Shadow Triangular Snake Graph

Let G = (V(G), E(G)) be a connected graph, where V(G) is the set of vertices and E(G) is the set of edges. The set Dt(G) is called the total domination set in G if every vertex v 2 V(G) is adjacent to at least one vertex in Dt (G). Furthermore, Dt(G) must satisfy the property N(Dt ) = V(G), where N(Dt) is an open neighbourhood set of Dt(G). Suppose that Dt(G) is the total domination set with minimum cardinality. If V(G) - Dt(G) contains a total domination set Dt-1(G), then Dt-1(G) is the inverse set of total domination relative to the total domination set Dt (G). The inverse’s number of the total domination set denotes the minimum cardinality of the inverse set of total domination. This number is denoted by gt-1 (G). This article discusses the inverse’s number of total domination of the triangular snake graph (Tn), line triangular snake graph (L (Tn)), and shadow triangular snake graph (D2 (Tn)). Graph Tn is a graph obtained from the path graph (Pn) by replacing each side of the path with a cycle graph (C3). Graph L (Tn) is a graph where the vertex set in L(Tn) is the edge set on Tn, or V(L(Tn)) = E(Tn). Graph D2 (Tn) is a graph obtained by combining two copies of a graph Tn, namely Tn0 and T00n. This research shows that the graph Tn does not have an inverse of domination total, gt-1 (L (Tn)) = n for n = 4, 6, 8, gt-1 (L (Tn)) = n - 1 for n = 3, 5, 7, or n ≥ 9 with n 2 N, and gt-1 (D2 (Tn)) = b23nc for n ≥ 3 with n 2 N.

Total 2-Rainbow Domination in Graphs

A total k-rainbow dominating function on a graph G=(V,E) is a function f:V(G)→2{1,2,…,k} such that (i) ∪u∈N(v)f(u)={1,2,…,k} for every vertex v with f(v)=∅, (ii) ∪u∈N(v)f(u)≠∅ for f(v)≠∅. The weight of a total 2-rainbow dominating function is denoted by ω(f)=∑v∈V(G)|f(v)|. The total k-rainbow domination number of G is the minimum weight of a total k-rainbow dominating function of G. The minimum total 2-rainbow domination problem (MT2RDP) is to find the total 2-rainbow domination number of the input graph. In this paper, we study the total 2-rainbow domination number of graphs. We prove that the MT2RDP is NP-complete for planar bipartite graphs, chordal bipartite graphs, undirected path graphs and split graphs. Then, a linear-time algorithm is proposed for computing the total k-rainbow domination number of trees. Finally, we study the difference in complexity between MT2RDP and the minimum 2-rainbow domination problem.

Probability of total domination for transient reflecting processes in a quadrant

AbstractWe consider two-dimensional Lévy processes reflected to stay in the positive quadrant. Our focus is on the non-standard regime when the mean of the free process is negative but the reflection vectors point away from the origin, so that the reflected process escapes to infinity along one of the axes. Under rather general conditions, it is shown that such behaviour is certain and each component can dominate the other with positive probability for any given starting position. Additionally, we establish the corresponding invariance principle providing justification for the use of the reflected Brownian motion as an approximate model. Focusing on the probability that the first component dominates, we derive a kernel equation for the respective Laplace transform in the starting position. This is done for the compound Poisson model with negative exponential jumps and, by means of approximation, for the Brownian model. Both equations are solved via boundary value problem analysis, which also yields the domination probability when starting at the origin. Finally, certain asymptotic analysis and numerical results are presented.

Maker-Breaker total domination game on cubic graphs

We study Maker--Breaker total domination game played by two players, Dominator and Staller, on the connected cubic graphs. Staller (playing the role of Maker) wins if she manages to claim an open neighbourhood of a vertex. Dominator wins otherwise (i.e.\ if he can claim a total dominating set of a graph). For certain graphs on $n\geq 6$ vertices, we give the characterization on those which are Dominator's win and those which are Staller's win.

Hannah Arendt, Baʿthism, and Anfal

AbstractIn the twentieth century, totalitarianism emerged as a new phenomenon, with powerful new regimes sweeping to power on the backs of the ideologies of National Socialism, Bolshevism, and Baʿthism. Armed with these ideologies, and in their names, such regimes committed murder at a mass scale previously unknown to world history. Among the victims of this historical process were the Kurds in Iraq, who were subjected to genocide at the hands of the Baʿthist regime. This article addresses the relationship between totalitarianism and genocide, and specifically how the Baʿthist regime justified genocide against the Kurds. It argues that three elements in Hannah Arendt's theory of totalitarianism –ideology, terror, and total domination – explain why every totalitarian regime in history has wound up resorting to genocidal programs. Using the 1980s Anfal campaign by the Baʿthist regime against the Kurds as a case study, this article elucidates the relationship between totalitarianism and genocide. This analysis will lead to a better understanding of the justifications, features, and motivations of the Baʿthist regime's genocide against Kurds.

On Secure Total Domination Cover Pebbling Number

In this paper, we introduce a new graph invariant called the secure total domination cover pebbling number, a combination of two graph invariants, namely, `secure total domination' and `cover pebbling number'. The secure total domination cover pebbling number of a graph \(G\), denoted by \(f_{stdp}(G)\), is the minimum number of pebbles that are required to place on \(V(G)\), such that after a sequence of pebbling moves, the set of vertices with pebbles forms a total secure dominating set under any configuration of pebbles to the vertices of graph \(G\). The secure total domination cover pebbling number for join of two graphs \(G(p,q)\) and \(G'(p',q')\) is determined. Also, a generalization of secure total domination cover pebbling number for some families of graphs such as complete graph \(K_n\), complete bipartite graph \(K_{p,q}\), complete $y$-partite graph \(K_{p_1,p_2,\ldots,p_y}\) and path \(P_n\) is found.