In 1966, Chartrand proved that if the minimum degree of a graph is at least the floor of half the number of nodes, then its edge-connectivity equals its minimum degree. A more discriminating notion of edge-connectivity is introduced, called the k -component order edge-connectivity, which is the minimum number of edges required to be removed so that the order of each component of the resulting subgraph is less than k . Results are established that guarantee that this parameter is at least as large as the minimum degree, provided the minimum degree is sufficiently large. This generalizes Chartrand's result. It is also determined when these results are best possible.
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ABSTRAKMeningkatnya jumlah sampah botol plastik sekarang ini telah membawa banyak masalah kesehatan dan lingkungan hidup. Masalah tersebut dapat dikurangi jika seseorang mau membawa botol minum (tumbler) sendiri. Namun, dibutuhkan mesin penjual air mineral untuk mengisi ulang tumbler. Paper ini menjelaskan disain dan implementasi prototipe mesin penjual air mineral otomatis, praktis, dan ekonomis berbasis Arduino Mega 2560 dan RFID-RC522. Pengujian terhadap prototipe ini dilakukan dalam tiga tahap: (1) pengujian jarak baca antara kartu RFID dengan RFID reader, (2) pengujian pada kondisi ideal, dan (3) pengujian pada kondisi tidak ideal. Dari pengujian pertama disimpulkan bahwa RFID-RC522 dapat melakukan pembacaan optimal pada jarak 35 mm. Dari hasil pengujian kedua diperoleh nilai akurasi (keakuratan) pada saat pengisian air sebesar 82%. Sedangkan hasil pengujian ketiga menyatakan bahwa prototipe dapat membaca kemungkinan yang terjadi pada kondisi tidak ideal. Kelemahan dari prototipe ini adalah belum terintegrasi dengan sistem pembayaran uang elektronik (e-money).Kata kunci: Arduino Mega 2560, Mikrokontroller, RFID-RC522, Sampah Plastik. ABSTRACTThe increasing amount of plastic bottle waste today has brought many health and environmental problems. These problem can be minimized when someone brings their own drinking bottle water. But, vending machine-like was needed to refill the tumbler. This paper explains a design implementation of prototype that can provide an automatic, practical, and economical mineral water filling based on Arduino Mega 2560 and RFID-RC522. Testing on this prototype was carried out in three stages: (1) testing of the reading distance between the RFID card and the RFID reader, (2) testing under ideal conditions, and (3) testing under non-ideal conditions. From the first test summarized that the RFID-RC522 can perform optimal readings at a distance of 35 mm. From the second test obtained the accuracy of the prototype when filling water by 82%. And the third test shows that the prototype could read the possibilities occurred in non-ideal conditions. The drawback of this prototype is not yet integrated with e-money payment system.Keywords: Arduino Mega 2560, Microcontroller, RFID-RC522, Plastic Waste.
Abstract.One of the key issues in designing a network topology is vulnerability. The vulnerability parameter measures the resistance of a network to disruption of operation after the failure of certain stations or communication links. One counter-measure to address the vulnerability of a network is edge connectivity. In this paper, a more selective concept of edge connectivity is introduced, called component order edge connectivity for MAN topology design. This parameter equals the smallest number of edges that must be removed in order to ensure that the order of each component of the resulting sub-network or sub-graph is less than k.
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