Amalgam

Amalgam — амальгама.

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.