Roman Domination in Complementary Prisms

The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect match- ing between the corresponding vertices of G and G. A Roman dominating function on a graph G = (V,E) is a labeling f : V(G) → {0,1,2} such that every vertex with label 0 is adjacent to a vertex with label 2. The Roman domination number γR(G) of G is the minimum f(V ) = Σv∈V f(v) over all such functions of G. We study the Roman domination number of complementary prisms. Our main results show that γR(GG) takes on a limited number of values in terms of the domination number of GG and the Roman domination numbers of G and G

Italian Domination in Complementary Prisms

Let $G$ be any graph and let $\overline{G}$ be its complement. The complementary prism of $G$ is formed from the disjoint union of a graph $G$ and its complement $\overline{G}$ by adding the edges of a perfect matching between the corresponding vertices of $G$ and $\overline{G}$. An Italian dominating function on a graph $G$ is a function such that $f \, : \, V \to \{ 0,1,2 \}$ and for each vertex $v \in V$ for which $f(v)=0$, it holds that $\sum_{u \in N(v)} f(u) \geq 2$. The weight of an Italian dominating function is the value $f(V)=\sum_{u \in V(G)}f(u)$. The minimum weight of all such functions on $G$ is called the Italian domination number. In this thesis we will study Italian domination in complementary prisms. First we will present an error found in one of the references. Then we will define the small values of the Italian domination in complementary prisms, find the value of the Italian domination number in specific families of graphs complementary prisms, and conclude with future problems

Italian Domination on Ladders and Related Products

An Italian dominating function on a graph $G = (V,E)$ is a function such that $f : V \to \{0,1,2\}$, and for each vertex $v \in V$ for which $f(v) = 0$, we have $\sum_{u\in N(v)}f(u) \geq 2$. The weight of an Italian dominating function is $f(V) = \sum_{v\in V(G)}f(v)$. The minimum weight of all such functions on a graph $G$ is called the Italian domination number of $G$. In this thesis, we will consider Italian domination in various types of products of a graph $G$ with the complete graph $K_2$. We will find the value of the Italian domination number for ladders, specific families of prisms, mobius ladders and related products including categorical products $G\times K_2$ and lexicographic products $G\cdot K_2$. Finally, we will conclude with open problems

Roman Domination in Complementary Prism Graphs

A Roman domination function on a complementary prism graph GGc is a function f : V [ V c ! {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2. The Roman domination number R(GGc) of a graph G = (V,E) is the minimum of Px2V [V c f(x) over such functions, where the complementary prism GGc of G is graph obtained from disjoint union of G and its complement Gc by adding edges of a perfect matching between corresponding vertices of G and Gc. In this paper, we have investigated few properties of R(GGc) and its relation with other parameters are obtaine

International Journal of Mathematical Combinatorics, Vol.6A

The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 460 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences

Art as integral part of architectural space

Thesis (M.S.V.S.)--Massachusetts Institute of Technology, Dept. of Architecture, 1993.Includes bibliographical references (leaves 93-97).To integrate art with architecture is the intention of every architect. However, many times other requirements overwhelm artistic potential. There are numerous good, simple examples in the history of architecture where solutions to a variety of often functional requirements have produced exceptional artistic expressions, which in tum have inspired contemporary architectural practice. Pre-industrial architecture not only responded to natural conditions in the environment; it employed all the senses as well ·. in its design of living environments. Today, unfortunately, we rarely find that architects pay attention to sound, smell, water, natural cycles, or, almost unimaginable, to time. Our technology encourages us to separate ourselves from nature. However, this same technology can help us to reintegrate ourselves with nature by designing better living environments. This thesis is, therefore, my way of rethinking design principles that shape the contemporary urban environment and often give it such a cold, formal image. My own philosophy of design is given in the introduction. The rest of the thesis is basically the supportive material, which further illuminates the ideas presented in the introduction. The first part discusses some general trends in contemporary society in order to place my own view of design within a broader context, while the second part lists numerous examples from the history of architecture and art to illustrate and further my philosophy. At the end, in the appendix, I present one of my own projects, the Interactive Water Curtain, to concretely show some of the implications of my aesthetics. Through this work I hope to illustrate the richness of various traditional architectural practices that take advantage of sound, water, time (celestial movement), fragrances, and even living creatures in designing places. I hope this will stimulate creative thinking about using not just visual effects in the design of our living environment, but employing acoustic, olfactory, astronomical, ecological, and kinesthetic design in order to create sensually richer and more pleasant environments where people can live in harmony with nature and other living creatures.by Marta Vahtar.M.S.V.S

The African social question: A challenge to the African church in light of the two synods on Africa

The First Synod of Catholic Bishops on Africa took place in April 1994 in the wake of the Rwandan genocide. That horrendous fratricide has left a dark spot in the history of Catholicism in Africa where “the blood of tribalism is thicker than the water of baptism”. The Second Synod on Africa, held in October 2009, had as its theme: “The Church in Africa in service to reconciliation, justice and peace”. Pope Benedict XVI issued a post-synodal exhortation, entitled Africae Munus. In one article, the pope writes: “Reconciliation is a way of life and mission of the Church” (Africae Munus no. 34). This article is set against that background to examine the mission and the role which the Catholic Church can play in Africa with regard to the African social question that encompasses all other perennial issues on the continent. Those other issues include ethnicity, religious and cultural hatred, as well as incessant conflicts that lead to the loss of lives andretardation in development

Custom and Tradition Versus Reason in Modern Secular and Religious Moral Reasoning and in Modern Constitutional Law

Custom and Tradition versus Reason in Modern Secular and Religious Moral Reasoning and in Modern Constitutional Law: Contemporary debates over values, the so-called “Culture Wars,” are best understood not as a debate between religious and secular ideologies, but rather a debate between traditional ideologies, whether religious or secular, which reflect customary or traditional norms, versus progressive ideology, whether religious or secular, which reflect rational deliberation about moral reasoning. Customary or traditional attitudes, both secular and religious, have supported, among other things, slavery, segregation and anti-miscegenation laws, denial of equal rights for women, anti-Semitism, rejection of the cosmology of Galileo, rejection of Darwinian evolution, limitations on access to birth control, limitations on stem-cell research, limitations on choice regarding abortion pre-viability, and denial of equal rights to gays and lesbians. In contrast, the perspective of adult reason commits one to the logical and rational elaboration of giving each individual what Ronald Dworkin has called “equal concern and respect,” reflected in religious traditions by rational elaboration of the biblical imperative of “love of neighbor as oneself,” or in classic Enlightenment terms by Adam Smith and the Scottish Enlightenment’s concept of behaving according to the logic of an “impartial spectator.” A major difference among Supreme Court Justices is the extent to which broad terms in the Constitution, like liberty or equality, should be read consistent with customary and traditional beliefs, a view supported by Justices Scalia and Thomas, or should be read in light of the demands of reason, the position of Justices Stevens, Kennedy, Souter, Ginsburg, and Breyer. The article addresses each of these points in greater depth

Liberation or Reconstruction: a critical survey on the relevance of Black theology in light of the emergence of Reconstruction theology

Magister Theologiae - MThThe purpose of this investigation is to discuss the relevance of Black theology in light of the emergence of reconstruction theology. It offers a critical survey of a range of contributions on this issue, questioning whether scholars who have used Black theology as a form of self description should shift emphasis, from the paradigm of liberation to reconstruction. The significance of this study has to be understood within the context of the proposal to redirect African theological initiatives from liberation theologies to reconstruction theology. The basis for this call was the end of apartheid in South Africa, which signalled the independence of all countries on the African continent.South Afric