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Given two plane trees \,T_{1} and \,T_{2}, with the same number of leaves and without degree 2 vertices, and a bijection \varphi between their leaf sets which preserves their order on the plane. The amalgam A =
{\mathcal A}(T_{1},T_{2}, \varphi) is the union of the corresponding Halin graphs {\mathcal H}(T_{1}) and {\mathcal H}(T_{2}) in which the leaf vertices \,v and \varphi(v) are identified.