• Korean Journal of Mathematics
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• 제27권3호
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• pp.563-580
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• 2019

In this paper, we study the strong metric dimension of zero-divisor graph ${\Gamma}(R)$ associated to a ring R. This is done by transforming the problem into a more well-known problem of finding the vertex cover number ${\alpha}(G)$ of a strong resolving graph $G_{sr}$. We find the strong metric dimension of zero-divisor graphs of the ring ${\mathbb{Z}}_n$ of integers modulo n and the ring of Gaussian integers ${\mathbb{Z}}_n$[i] modulo n. We obtain the bounds for strong metric dimension of zero-divisor graphs and we also discuss the strong metric dimension of the Cartesian product of graphs.

• JSTS:Journal of Semiconductor Technology and Science
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• 제16권6호
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• pp.832-841
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• 2016

The voltage-frequency island (VFI) design paradigm has strong potential for achieving high energy efficiency in communication centric manycore system-on-chip (SoC) design called network-on-chip (NoC). However, because of the diminished scaling of wire-dimension and supply voltage as well as threshold voltage in modern CMOS technology, the vulnerability to link failure in VFI NoC is becoming a crucial challenge. In this paper, we propose an energy-optimized topology generation technique for VFI NoC to cope with permanent link failures. Based on the energy consumption model, we exploit the on-chip communication traffic patterns and characteristics of link failures in the early design stage to accommodate diverse applications and architectures. Experimental results using a number of multimedia application benchmarks show the effectiveness of the proposed three-step custom topology generation method in terms of energy consumption and latency without any degradation in the fault coverage metric.