Magic polygon

A magic polygon is a polygonal magic graph with integers on its vertices.

Perimeter magic polygon
A magic polygon, also called a perimeter magic polygon, is a polygon with an integers on its sides that all add up to a magic constant. It is where positive integers (from 1 to N) on a k-sided polygon add up to a constant. Magic polygons are a generalization of other magic shapes such as magic triangles.

Magic polygon with a center point
Victoria Jakicic and Rachelle Bouchat defined magic polygons as n-sided regular polygons with 2n+1 nodes such that the sum of the three nodes are equal. In their definition, a 3&thinsp;×&thinsp;3 magic square can be viewed as a magic 4-gon. There are no magic odd-gons with this definition.

Magic polygons and degenerated magic polygons
Danniel Dias Augusto and Josimar da Silva defined the magic polygon P(n,k) as a set of vertices of $$k/2$$ concentric n-gon and a center point. In this definition, magic polygons of Victoria Jakicic and Rachelle Bouchat can be viewed as P(n,2) magic polygons. They also defined degenerated magic polygons.