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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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