Amalgam

Amalgam — амальгама.

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