Abstract
We know that supercomputers include thousands of processors, all of which are large-scale parallel systems, it is known that interconnection network is an important part of supercomputer, which usually can determine the performance of parallel computer. But with the increase in size and processing speed, it is inevitable that some processors in such a system may fail. In order to measure the reliability of the system, we should study how to measure the advantages and disadvantages of these networks. So we need to study the reliability of the networks. Typically, the mathematical model of an interconnection network is a connected graph where the vertices usually corresponding to processors and the edges corresponding to the communication links between the processors. Such a close relation between graph theory and interconnection network motivates us to investigate the domination stability of graphs. Domination number is one of the important parameters to measure the performance of network topology, based on this, in this paper we study the domination number of the graph. We also consider the effect of edge operations on the domination number, i.e., the bondage number, it is a measure of vulnerability of the interconnection network under link failure. The domination number and bondage number for arbitrary graphs is NP-complete, so in this paper we mainly focus on two parameters-domination number and bondage number for the middle graph of the fan graph. Finally we obtain two theories.
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Acknowledgment
This work was supported by the National Key R&D Program of China (grant 2018YFB0803700), the fundamental Research Funds for the Central Universities, Beijing Municipal Natural Science Foundation (4212019) and Guangxi Key Laboratory of Cryptography and Information Security (No GCIS201808).
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Cao, J. (2022). Reliability Research of a Class of Networks. In: Li, X. (eds) Advances in Intelligent Automation and Soft Computing. IASC 2021. Lecture Notes on Data Engineering and Communications Technologies, vol 80. Springer, Cham. https://doi.org/10.1007/978-3-030-81007-8_115
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DOI: https://doi.org/10.1007/978-3-030-81007-8_115
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