I need help understanding this Lemma and proof.
Lemma
Let $G$ be the graph obtained from a graph $G_1$ by identifying an arbitrary vertex of $G_1$ and one pendent vertex of the path $P_2.$
Then the determinant of the distance matrix of the graph $G$ is fixed, regardless the
choice of the vertex of $G.$
Does $P_2$ mean chordless path on $2$ vertices? Does identifying vertices mean contracting them in one vertex which has edges to all vertices that these two had? How is it possible that then $G_1$ is subgraph of $G$ when $G$ was obtained from $G_1$ by identifying vertices?