Independent Verification of Euler’s Formula in Graph Theory for n identical circles

Abstract

This paper discusses the famous Euler’s formula in graph theory and its independent verification for the case of n identical circles forming a planar graph. A planar connected graph is generated using n circles, and an intuitive approach is taken to construct formulae for the number of vertices (v), edges (e) and faces (f), where symmetry of the pattern is used to determine the relation between v, e and f.