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'''Amalgamation of a graph''' — ''[[амальгамация графа]].'' 

Amalgamating a [[graph, undirected graph, nonoriented graph|graph]] <math>\,H</math> can be thought of as taking <math>\,H</math>, partitioning
its [[vertex|vertices]], then, for each element of the partition, squashing
together the vertices to form a single vertex in the amalgamated graph
<math>\,G</math>. Any [[edge|edges]] incident with original vertices in <math>\,H</math> are then
incident with the corresponding new vertex in <math>\,G</math>, and any edge
joining two vertices that are squashed together in <math>\,H</math> becomes a
loop on the new vertex in <math>\,G</math>. The number of vertices squashed
together to form a new vertex <math>\,w</math> is the '''amalgamation number'''
<math>\,\eta(w)</math> of <math>\,w</math>. The resulting graph is the '''amalgamation''' of the
original. Formally, this is represented by a graph homomorphism <math>f:
V(G) \rightarrow V(H)</math>; so for example if <math>w \in V(H)</math>, then <math>\,\eta(w)
= |f^{-1}(w)|</math>.