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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
UK Rules For Unfired Pressure Vessels
The present code PD 5500, formerly BS 5500 [1] evolved partly from the well-known BS 1500 [2] in the 1950's and BS 1515 [3] first published in 1965; the latter permitted higher level allowable stresses and more advanced rules. In 1969, following a report from the Committee of Enquiry into the Pressure Vessel Industry, the British Standards Institution brought all the pressure vessel interests together under one general committee in order to rationalise the activity. This became PVE/ and presides over a large committee structure. There are a series of functional sub-committees who deal with specific aspects and a large number of technical committees as well as many additional sub committees and working groups. Most of these meet regularly. The technical committee PVE/1, Pressure Vessels, has overall responsibility for BS 5500. The functional committee PVE/1/15 Design Methods has an overall responsibility relating to 'Design' with particular reference to the design section of BS 5500 (Section 3). The first edition of BS 5500 was issued in 1976. The actual issue was delayed for some time because, in the early 1970's, there was an attempt in Europe to produce an international pressure vessel standard. A draft of the international standard appeared as ISO DIS 2694 [4] in 1973 but it was not generally accepted and the attempt was abandoned in the mid 70's. It was decided to use some of the material from 2694 within BS 5500 so that although the Standard was long delayed it benefited to some extent from the international efforts. Initially, committee PVE/l set out the concept of a "master" pressure vessel standard which could readily be applied to any vessel in either ferrous or non-ferrous materials and for highly specialised application with the minimum of supplementary requirements. The layout of BS 5500 is consistent with this concept and although the Standard has perhaps not fulfilled this high ideal, it has certainly been employed widely in many industries including non pressure vessel type applications. When issued it had a number of distinctive features compared with other pressure codes viz; weld joint factors were removed, the present three categories of construction were introduced, there was a new novel external pressure section, it has a loose leaf format and an annual updating was introduced. Further editions of BS 5500 have been issued every three years since 1982
Restrained reinforcement number in graphs
A set of vertices is a restrained dominating set of a graph if every vertex in has a neighbor in and a neighbor in . The minimum cardinality of a restrained dominating set is the restrained domination number . In this paper we initiate the study of the restrained reinforcement number of a graph defined as the cardinality of a smallest set of edges for which $\gamma _{r}(G+F
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