Outer independent double Roman domination Abdollahzadeh Ahangar, H.; Chellali, M.; Sheikholeslami, S.M.
Applied mathematics and computation,
01/2020, Volume:
364
Journal Article
Peer reviewed
An outer independent double Roman dominating function (OIDRDF) of a graph G is a function h from V(G) to {0, 1, 2, 3} for which each vertex with label 0 is adjacent to a vertex with label 3 or at ...least two vertices with label 2, and each vertex with label 1, is adjacent to a vertex with label greater than 1; and all vertices labeled by 0 is independent. The weight of an OIDRDF h is ∑w ∈ V(G)h(w), and the outer independent double Roman domination number γoidR(G) is the minimum weight of an OIDRDF on G. In this article, we provide various bounds on γoidR(G) and we show that its determining is NP-complete on chordal and bipartite graphs. Moreover, we establish Nordhaus–Gaddum bounds for γoidR(G)+γoidR(G¯).
The legendary overland silk road was not the only way to reach Asia for ancient travelers from the Mediterranean. During the Roman Empire’s heyday, equally important maritime routes reached from the ...Egyptian Red Sea across the Indian Ocean. The ancient city of Berenike, located approximately 500 miles south of today’s Suez Canal, was a significant port among these conduits. In this book, Steven E. Sidebotham, the archaeologist who excavated Berenike, uncovers the role the city played in the regional, local, and “global” economies during the eight centuries of its existence. Sidebotham analyzes many of the artifacts, botanical and faunal remains, and hundreds of the texts he and his team found in excavations, providing a profoundly intimate glimpse of the people who lived, worked, and died in this emporium between the classical Mediterranean world and Asia.
Nigeria is a country shaped by internal diversity and transnational connections, past and present. Leading Nigerian writers from Chinua Achebe, Amos Tutuola and Wole Soyinka to Chimamanda Ngozi ...Adichie and Teju Cole have portrayed these Nigerian issues, and have also written about some of the momentous events in Nigerian history. Afropolitan Horizons discusses their work alongside other novelists and commentators, as well as describing the ways in which Nigeria has appeared in foreign news reporting. It is all interwoven with the author’s own anthropological field research in a town in Central Nigeria.
Experts explore what factors drove the emergence of scale as a defining element in ancient Italian architecture, and how these factors influenced the origins and development of Etruscan and early ...Roman monumental designs.
Modern America owes the Roman Empire for more than gladiator movies and the architecture of the nation's Capitol. It can also thank the ancient republic for some helpful lessons in globalization. So ...argues economic historian Harold James in this masterful work of intellectual history.
The book addresses what James terms "the Roman dilemma"--the paradoxical notion that while global society depends on a system of rules for building peace and prosperity, this system inevitably leads to domestic clashes, international rivalry, and even wars. As it did in ancient Rome, James argues, a rule-based world order eventually subverts and destroys itself, creating the need for imperial action. The result is a continuous fluctuation between pacification and the breakdown of domestic order.
James summons this argument, first put forth more than two centuries ago in Adam Smith'sWealth of Nationsand Edward Gibbon'sDecline and Fall of the Roman Empire, to put current events into perspective. The world now finds itself staggering between a set of internationally negotiated trading rules and exchange--rate regimes, and the enforcement practiced by a sometimes-imperial America. These two forces--liberal international order and empire--will one day feed on each other to create a shakeup in global relations, James predicts. To reinforce his point, he invokes the familiarbon motonce applied to the British Empire:"When Britain could not rule the waves, it waived the rules."
Despite the pessimistic prognostications of Smith and Gibbon, who saw no way out of this dilemma, James ends his book on a less depressing note. He includes a chapter on one possible way in which the world could resolve the Roman Predicament--by opting for a global system based on values as opposed to rules.
Why have Americans expressed concern about immigration at some
times but not at others? In pursuit of an answer, this book
examines America's first nativist movement, which responded to the
rapid ...influx of 4.2 million immigrants between 1840 and 1860 and
culminated in the dramatic rise of the National American Party. As
previous studies have focused on the coasts, historians have not
yet completely explained why westerners joined the ranks of the
National American, or "Know Nothing," Party or why the nation's
bloodiest anti-immigrant riots erupted in western cities-namely
Chicago, Cincinnati, Louisville, and St. Louis. In focusing on the
antebellum West, Inventing America's First Immigration
Crisis illuminates the cultural, economic, and political
issues that originally motivated American nativism and explains how
it ultimately shaped the political relationship between church and
state. In six detailed chapters, Ritter explains how unprecedented
immigration from Europe and rapid westward expansion reignited
fears of Catholicism as a corrosive force. He presents new research
on the inner sanctums of the secretive Order of Know-Nothings and
provides original data on immigration, crime, and poverty in the
urban West. Ritter argues that the country's first bout of
political nativism actually renewed Americans' commitment to
church-state separation. Native-born Americans compelled Catholics
and immigrants, who might have otherwise shared an affinity for
monarchism, to accept American-style democracy. Catholics and
immigrants forced Americans to adopt a more inclusive definition of
religious freedom. This study offers valuable insight into the
history of nativism in U.S. politics and sheds light on present-day
concerns about immigration, particularly the role of anti-Islamic
appeals in recent elections.
Double Roman domination Beeler, Robert A.; Haynes, Teresa W.; Hedetniemi, Stephen T.
Discrete Applied Mathematics,
10/2016, Volume:
211
Journal Article
Peer reviewed
Open access
For a graph G=(V,E), a double Roman dominating function is a function f:V→{0,1,2,3} having the property that if f(v)=0, then vertex v must have at least two neighbors assigned 2 under f or one ...neighbor with f(w)=3, and if f(v)=1, then vertex v must have at least one neighbor with f(w)≥2. The weight of a double Roman dominating function f is the sum f(V)=∑v∈Vf(v), and the minimum weight of a double Roman dominating function on G is the double Roman domination number of G. We initiate the study of double Roman domination and show its relationship to both domination and Roman domination. Finally, we present an upper bound on the double Roman domination number of a connected graph G in terms of the order of G and characterize the graphs attaining this bound.
Maximal double Roman domination in graphs Abdollahzadeh Ahangar, H.; Chellali, M.; Sheikholeslami, S.M. ...
Applied mathematics and computation,
02/2022, Volume:
414
Journal Article
Peer reviewed
•We introduce maximal double Roman dominating functions in graphs and study the corresponding parameter γdRm(G).•We show that the problem of determining γdRm(G) is NP-complete for bipartite, chordal ...and planar graphs. But it is solvable in linear time for bounded clique-width graphs including trees, cographs and distance-hereditary graphs.•We establish various relationships relating γdRm(G) to some domination parameters.•For the class of trees, we show that for every tree T of order n≥4,γdRm(T)≤54n and we characterize all trees attaining the bound.•Finally, the exact values of γdRm(G) are given for paths and cycles.
A maximal double Roman dominating function (MDRDF) on a graph G=(V,E) is a function f:V(G)→{0,1,2,3} such that (i) every vertex v with f(v)=0 is adjacent to least two vertices assigned 2 or to at least one vertex assigned 3, (ii) every vertex v with f(v)=1 is adjacent to at least one vertex assigned 2 or 3 and (iii) the set {w∈V|f(w)=0} is not a dominating set of G. The weight of a MDRDF is the sum of its function values over all vertices, and the maximal double Roman domination number γdRm(G) is the minimum weight of an MDRDF on G. In this paper, we initiate the study of maximal double Roman domination. We first show that the problem of determining γdRm(G) is NP-complete for bipartite, chordal and planar graphs. But it is solvable in linear time for bounded clique-width graphs including trees, cographs and distance-hereditary graphs. Moreover, we establish various relationships relating γdRm(G) to some domination parameters. For the class of trees, we show that for every tree T of order n≥4,γdRm(T)≤54n and we characterize all trees attaining the bound. Finally, the exact values of γdRm(G) are given for paths and cycles.
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