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Existence of holey LSSOM of type 2n with application to G7-packings of Kv
Institution:1. MIS Area, Indian Institute of Management, Tiruchirappalli, India;2. School of Management, Gautam Buddha University, Greater Noida, UP, India;1. State Key Laboratory of Power Systems, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China;2. CHN Energy ZhiShen Control Technology Co., Ltd. (Beijing Engineering Research Center of Power Station Automation), Beijing 102211, China;3. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;4. National Engineering Research Center of Power Generation Control and Safety, School of Energy and Environment, Southeast University, Nanjing 210096, China;5. Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China
Abstract:In this paper, we show that the set of all integers n⩾4 is the spectrum of two mutually orthogonal holey Latin squares, of type 2n, in which one square is symmetric. As an application, we determine the maximum number of pairwise edge disjoint copies of G7 in Kv for each v, and all possible graphs that arise from the unused edges.
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