Abstract
Let G = (V (G), E(G)) be a simple connected graph of order n. For any vertices u, v,w ∈ V (G) with uv ∈ E(G) and uw ∈ E(G), an edge-rotating of G means rotating the edge uv (around u) to the non-edge position uw. In this work, we consider how the least eigenvalue of a graph perturbs when the graph is performed by rotating an edge from the shorter hanging path to the longer one.
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Supported by the National Natural Science Foundation of China (No. 11201432, No. 11301440), and the Natural Science Foundation of Education Ministry of Henan Province (No. 15A110003, No. 15IRTSTHN006, No. 13B110939).
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Liu, Rf., Jia, Hc. & Shu, Jl. An edge-rotating theorem on the least eigenvalue of graphs. Acta Math. Appl. Sin. Engl. Ser. 31, 945–952 (2015). https://doi.org/10.1007/s10255-015-0512-2
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DOI: https://doi.org/10.1007/s10255-015-0512-2