For a graph G=(V,E) with V=V(G) and E=E(G), a Roman {3}-dominating function is a function f:V→{0,1,2,3} having the property that ∑u∈NG(v)f(u)≥3, if f(v)=0, and ∑u∈NG(v)f(u)≥2, if f(v)=1 for any ...vertex v∈G. The weight of a Roman {3}-dominating function f is the sum f(V)=∑v∈V(G)f(v) and the minimum weight of a Roman {3}-dominating function on G is the Roman {3}-domination number of G, denoted by γ{R3}(G). We initiate the study of Roman {3}-domination and show its relationship to domination, Roman domination, Roman {2}-domination (Italian domination) and double Roman domination. Finally, we present an upper bound on the Roman {3}-domination number of a connected graph G in terms of the order of G and characterize the graphs attaining this bound. Finally, we show that associated decision problem for Roman {3}-domination is NP-complete, even for bipartite graphs.
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Was there ever such a thing as Byzantium? Certainly no emperor ever called himself Byzantine. While the identities of eastern minorities were clear, that of the ruling majority remains obscured ...behind a name made up by later generations. Anthony Kaldellis says it is time for the Romanness of these so-called Byzantines to be taken seriously.
This book examines how Romans used their pottery and the implications of these practices on the archaeological record. It is organized around a flow model for the life cycle of Roman pottery that ...includes a set of eight distinct practices: manufacture, distribution, prime use, reuse, maintenance, recycling, discard, reclamation. J. Theodore Peña evaluates how these practices operated, how they have shaped the archaeological record, and the implications of these processes on archaeological research through the examination of a wide array of archaeological, textual, representational and comparative ethnographic evidence. The result is a rich portrayal of the dynamic that shaped the archaeological record of the ancient Romans that will be of interest to archaeologists, ceramicists, and students of material culture.
Why do spies have such cachet in the twentieth century? Why do they keep reinventing themselves? What do they mean in a political process? This book examines the tradition of the spy narrative from ...its inception in the late nineteenth century through the present day. Ranging from John le Carré's bestsellers to Elizabeth Bowen's novels, from James Bond to John Banville's contemporary narratives, Allan Hepburn sets the historical contexts of these fictions: the Cambridge spy ring; the Profumo Affair; the witch-hunts against gay men in the civil service and diplomatic corps in the 1950s.
Instead of focusing on the formulaic nature of the genre,Intrigueemphasizes the responsiveness of spy stories to particular historical contingencies. Hepburn begins by offering a systematic theory of the conventions and attractions of espionage fiction and then examines the British and Irish tradition of spy novels. A final section considers the particular form that American spy narratives have taken as they have cross-fertilized with the tradition of American romance in works such as Joan Didion'sDemocracyand John Barth'sSabbatical.
This exciting new study draws on objects excavated or discovered in the late nineteenth or early twentieth century at three Mediterranean sites. Through the three case studies,Materia ...Magicaidentifies specific forms of magic that may be otherwise unknown. It isolates the practitioners of magic and examines whether magic could be used as a form of countercultural resistance. Andrew T. Wilburn discovers magic in the objects of ancient daily life, suggesting that individuals frequently turned to magic, particularly in crises. Local forms of magic may have differed, and Wilburn proposes that the only way we can find small-town sorcerers is through careful examination of the archaeological evidence.
Studying the remains of spells enacted by practitioners, Wilburn's work unites the analysis of the words written on artifacts and the physical form of these objects. He situates these items within their contexts, to study how and why they were used.Materia Magicaapproaches magic as a material endeavor, in which spoken spells, ritual actions, and physical objects all played vital roles in the performance of a rite.
Materia Magicadevelops a new method for identifying and interpreting the material remains of magical practice by assessing artifacts within their archaeological contexts. Wilburn suggests that excavations undertaken in recent centuries can yield important lessons about the past, and he articulates the ways in which we can approach problematic data.
The Holy Roman Empire was one of the oldest and largest states in early modern Europe. This book breaks new ground in its collective exploration of the Empire's political and diplomatic, social and ...cultural relations and of transnational interactions.
Roman {2}-domination Chellali, Mustapha; Haynes, Teresa W.; Hedetniemi, Stephen T. ...
Discrete Applied Mathematics,
05/2016, Volume:
204
Journal Article
Peer reviewed
In this paper, we initiate the study of a variant of Roman dominating functions. For a graph G=(V,E), a Roman {2}-dominating function f:V→{0,1,2} has the property that for every vertex v∈V with ...f(v)=0, either v is adjacent to a vertex assigned 2 under f, or v is adjacent to least two vertices assigned 1 under f. The weight of a Roman {2}-dominating function is the sum ∑v∈Vf(v), and the minimum weight of a Roman {2}-dominating function f is the Roman {2}-domination number. First, we present bounds relating the Roman {2}-domination number to some other domination parameters. In particular, we show that the Roman {2}-domination number is bounded above by the 2-rainbow domination number. Moreover, we prove that equality between these two parameters holds for trees and cactus graphs with no even cycles. Finally, we show that associated decision problem for Roman {2}-domination is NP-complete, even for bipartite graphs.
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The slave experience was a defining one in American history, and not surprisingly, has been a significant and powerful trope in African American literature. In Re-Forming the Past, A. Timothy ...Spaulding examines contemporary revisions of slave narratives that use elements of the fantastic to redefine the historical and literary constructions of American slavery. In their rejection of mimetic representation and traditional historiography, postmodern slave narratives such as Ishmael Reed’s Flight to Canada, Octavia Butler’s Kindred, Toni Morrison’s Beloved, Charles Johnson’s Ox Herding Tale and Middle Passage, Jewelle Gomez’s The Gilda Stories, and Samuel Delaney’s Stars in My Pocket Like Grains of Sand set out to counter the usual slave narrative’s reliance on realism and objectivity by creating alternative histories based on subjective, fantastic, and non-realistic representations of slavery. As these texts critique traditional conceptions of history, identity, and aesthetic form, they simultaneously re-invest these concepts with a political agency that harkens back to the original project of the 19th-century slave narratives. In their rejection of mimetic representation and traditional historiography, Spaulding contextualizes postmodern slave narrative. By addressing both literary and popular African American texts, Re-Forming the Past expands discussions of both the African American literary tradition and postmodern culture.
The Roman Empire was based on law, and it was vital for rulers and ruled that laws should be understood. They were often given permanent form in stone or bronze. This book transcribes, translates, ...and fully illustrates with photographs, the inscription (more than 155 lines, in its damaged state) that carries the regulations drawn up over nearly two centuries for the customs dues of the rich province of Asia (western Turkey). The regulations, taken from Roman archives, were set up in Greek in Ephesus, and the book provides a rendering of the text back into Latin. The damaged text is hard to restore and to interpret. Six scholars offer line-by-line commentary, and five essays bring out its significance, from the Gracchi to Nero, for Rome's government and changing attitudes towards provincial subjects, for the historical geography of the Empire, for its economic history, and for the social life of Roman officials.
Since antiquity, the she-wolf has served as the potent symbol of Rome. For more than two thousand years, the legendary animal that rescued Romulus and Remus has been the subject of historical and ...political accounts, literary treatments in poetry and prose, and visual representations in every medium. In She-Wolf: The Story of a Roman Icon, Cristina Mazzoni examines the evolution of the she-wolf as a symbol in western history, art, and literature, from antiquity to contemporary times. Used, for example, as an icon of Roman imperial power, papal authority, and the distance between the present and the past, the she-wolf has also served as an allegory for greed, good politics, excessive female sexuality, and, most recently, modern, multi-cultural Rome. Mazzoni engagingly analyzes the various role guises of the she-wolf over time in the first comprehensive study in any language on this subject.
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