Consider the plane figure obtained by drawing each diagonal in a regular polygon with n vertices. If each point of intersection is associated with a node and diagonals are split ar each intersection to form segments associated with edges, the resulting figure is a planar graph here termed the polygon diagonal intersection graph and denoted R_n. For n = 1, 2, ..., the vertex counts v_n of R_n are 1, 2, 3, 5, 10, 19, 42, 57, 135, 171, ... (OEIS A007569), which are given by a finite sum of δ_m(n) = {1 | if n congruent 0 (mod m) 0 | otherwise. auto right match times polynomials in n with m = 2, 4, 6, 12, 18, 24, 30, 42, 60, 84, 90, 120, and 210.
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