WEAK TANGENTS ON CLOSED POPCORN GRAPHS

Abstract

Given [Formula: see text], we study the Assouad dimension and weak tangents of closed [Formula: see text]-popcorn graphs. For all [Formula: see text], we prove that [Formula: see text] is a weak tangent of the closed [Formula: see text]-popcorn graphs by using some arguments on prime numbers. For all [Formula: see text], we first show that the Assouad dimension of the closed [Formula: see text]-popcorn graphs is 1, and then prove that [Formula: see text] is a weak tangent of them. We also discuss some specific weak tangents of closed [Formula: see text]-popcorn graphs when [Formula: see text] and [Formula: see text].