Sun–Wang–Yao conjecture on transforming strongly graceful trees into paths

Let $T$ be a tree with a perfect matching. An edge-mismatched transfer-operation removes an edge $uv$ from $T$ and adds a non-edge $xy$ when the edges $uv$ and $xy$ have the same edge label under a strongly graceful labeling, producing a graph denoted $T-uv+xy$. A tree has a strongly graceful labeling when its vertex labels induce the required distinct edge labels and complementary labels on the endpoints of each matching edge. Sun–Wang–Yao's conjecture. Any tree with a perfect matching can be transformed into some path with a perfect matching by a sequence of edge-mismatched transfer-operations such that both the original tree and the resulting path admit strongly graceful labelings. This conjecture proposes a reduction of strongly graceful trees with perfect matchings to paths via the stated operation; its resolution is not established in the supplied source.