On the intersection graph of the disks with diameters the sides of a convex <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si32.svg"><mml:mi>n</mml:mi></mml:math>-gon

Given a convex n-gon, we can draw n disks (called side disks) where each disk has different of the polygon as diameter and midpoint its center. The intersection graph such is undirected with vertices two are adjacent if only they have point in common. Such was introduced by Huemer Pérez-Lantero (Discrete Mathematics, 2020), proved to be planar Hamiltonian. In this paper, study further combinatorial properties graph. We prove that treewidth at most 3, showing an O(n)-time algorithm builds tree decomposition width given input. This implies construct O(n) time. independence number, which maximum number pairwise disjoint disks. planarity condition for every n-gon select least ⌈n/4⌉ disks, n≥3 there exist n-gons cannot more than number. Finally, show our class graphs includes all outerplanar Hamiltonian except cycle length four, it proper subclass graphs.