摘要
Let G = (V(G), E(G)) be a simple connected graph of order n. For any vertices u, v, w is an element of V(G) with uv is an element of E(G) and uw is not an element of 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.