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On minimally 2-(edge)-connected graphs with extremal spectral radius
Affiliation:1. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China;2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;3. School of Mathematical Sciences and LPMC, NanKai University, Tianjin, 300071, China;1. School of Mathematics and Finance, Chuzhou University, Chuzhou, Anhui 239012, China;2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, China;3. College of Mathematics and Systems Science, Xinjiang University, Urumqi, Xinjiang 830046, China;1. School of Mathematics and Finance, Chuzhou University, Chuzhou, Anhui 239012, China;2. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China;1. Department of Mathematics, East China University of Science and Technology, Shanghai, PR China;2. Department of Computer Science and Technology, East China Normal University, Shanghai, PR China
Abstract:A graph is minimally 2-(edge)-connected if it is 2-(edge)-connected and deleting any arbitrary chosen edge always leaves a graph which is not 2-(edge)-connected. In this paper, we completely characterize the minimally 2-(edge)-connected graphs having the largest and the smallest spectral radius, respectively.
Keywords:Minimally 2-connected graph  Minimally 2-edge-connected graph  Spectral radius  Extremal graph
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