= Branch vertex of a graph subdivision
= Branch vertices of a graph subdivision
{synonym}
A <branch vertex of a graph subdivision> is a retained original <vertex> in a specified <graph subdivision>. Its <degree of a vertex> in that <graph subdivision> equals its original <degree of a vertex>. It need not have <degree of a vertex> at least three: $B,C,D$ in the example are also <branch vertices of a graph subdivision>. When the target itself has <vertices> of <degree of a vertex> two, adjacency alone need not identify which <vertices> were original; the specified target mapping supplies that distinction.
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