A Note on the Edge Reconstruction Conjecture

We proved that if a graph \(G\) of minimum valency \(\delta=6\alpha + 5\), with \(\alpha\) a non-negative integer, can triangulate a surface \(\Sigma\) with \(\chi(\Sigma) = -\alpha n + \beta\), where \(\beta \in \{0, 1, 2\}\), then \(G\) is edge reconstructible.