Restrained reinforcement number in graphs

A set $S$ of vertices is a restrained dominating set of a graph $G=(V,E)$ if every vertex in $V\setminus S$ has a neighbor in $S$ and a neighbor in $V\setminus S$. The minimum cardinality of a restrained dominating set is the restrained domination number $\gamma_{r}(G)$. In this paper we initiate the study of the restrained reinforcement number $r_{r}(G)$ of a graph $G$ defined as the cardinality of a smallest set of edges $F\subseteq E(\overline{G})$ for which $\gamma _{r}(G+F

Protecting a Graph with Mobile Guards

Mobile guards on the vertices of a graph are used to defend it against attacks on either its vertices or its edges. Various models for this problem have been proposed. In this survey we describe a number of these models with particular attention to the case when the attack sequence is infinitely long and the guards must induce some particular configuration before each attack, such as a dominating set or a vertex cover. Results from the literature concerning the number of guards needed to successfully defend a graph in each of these problems are surveyed.Comment: 29 pages, two figures, surve

RESTRAINED ROMAN REINFORCEMENT NUMBER IN GRAPHS

A restrained Roman dominating function (RRD-function) on a graph $G=(V,E)$ is a function $f$ from $V$ into $\{0,1,2\}$ satisfying: (i)  every vertex $u$ with $f(u)=0$ is adjacent to a vertex $v$ with $f(v)=2$; (ii) the subgraph induced by the vertices assigned 0 under $f$ has no isolated vertices. The weight of an RRD-function is the sum of its function value over the whole set of vertices, and the restrained Roman domination number is the minimum weight of an RRD-function on $G.$ In this paper, we begin the study of the restrained Roman reinforcement number $r_{rR}(G)$ of a graph $G$ defined as the cardinality of a smallest set of edges that we must add to the graph to decrease its restrained Roman domination number. We first show that the decision problem associated with the restrained Roman reinforcement problem is NP-hard. Then several properties as well as some sharp bounds of the restrained Roman reinforcement number are presented. In particular it is established that $r_{rR}(T)=1$ for every tree $T$ of order at least three

The Cowl - v.82 - n.22 - Apr 19, 2018

The Cowl - student newspaper of Providence College. Volume 82, Number 22 - April 19, 2018. 28 pages

A Queer Series of Events: A Comparative Examination of Same-Sex Marriage Legalization

As of 2020, same-sex marriage has been legalized at the national level in 28 countries. This dissertation examines the factors that make legalization of same-sex marriage (same-sex marriage) more likely. Using quantitative analysis and a customized index, The Rainbow Index, to capture overall country friendliness towards LGB equality, this dissertation shows that a combination of secular and emancipative values, a high degree of LGB mobilization capacity, and opportunities for transnational advocacy networks to connect with and support local activists make legalization more likely. Furthermore, this combination of variables, which together represent a country’s friendliness to LGB equality, is more predictive of same-sex marriage legalization than the effects of modernization. Case study qualitative analysis drawing from the cases of Colombia, Japan, Mexico, and Taiwan will also be conducted based on the quantitative findings

Dramatising Social Care:Applied Theatre as a Tool of Empowerment for Looked After Children

This research examines the contextual layers and concentric frames that define the worlds of looked after children within contemporary British care systems in the search for an empowering, creative practice. This investigation has used practice as research to examine the current cultures, power relations and corporate contexts that intermesh to construct the care system. The core group of this enquiry is looked after children but, as an expanding 12 year action research model, the investigation examines the concurrent trends between children in care, children living in poverty and incarcerated young people. The use of macro and micro practice examples enables the thesis to examine the life cycles, trappings and pitfalls for contemporary poor law children as well as demonstrating how creative practice can impact on interventionist approaches to research and development, before young people end up in care. The potential for applied theatre as a tool for empowerment is interrogated through an exploration of what empowerment means in terms of radical freedom as well as the necessity of changes to existing structures and dominant assumptions. This research examines the different shapes, forms and possibilities for this practice from processes of inner discovery to narrative therapies, to collective encounters, to performances to relevant audiences. This research constructs a clear proposal for the efficacy of applied theatre/arts within these arenas and offers a colourful and innovative contribution to this field of knowledge through a range of rich and varied practice experiences and ethnographical sources.EThOS - Electronic Theses Online ServiceGBUnited Kingdo