Bulletin of Pure & Applied Sciences- Mathematics and Statistics
  • Year: 2018
  • Volume: 37e
  • Issue: 1

Independent verification of Euler'S formula in graph theory for n identical circles

1Department of Physics, G.B. Tatha Tatyasaheb Khare Commerce, Parvatibai Gurupad Dhere Arts and Shri. Mahesh Janardan Bhosale Science College, Guhagar, Dist. Ratnagiri (M.S.) India-415703 E-mail: padphy@gmail.com

2Department of Mathematics, G.B. Tatha Tatyasaheb Khare Commerce, Parvatibai Gurupad Dhere Arts and Shri. Mahesh Janardan Bhosale Science College, Guhagar, Dist. Ratnagiri (M.S.) India-415703 E-mail: yadav.abhijeet50@gmail.com

*Corresponding Author: Padmanabh S. Sarpotdar, Department of Physics, G.B. Tatha Tatyasaheb Khare Commerce, Parvatibai Gurupad Dhere Arts and Shri. Mahesh Janardan Bhosale Science College, Guhagar, Dist. Ratnagiri (M.S.) India-415703, E-mail: padphy@gmail.com

2010 AMS Mathematics Subject Classification: Primary: 44A10, 44A45 Secondary: 33B10, 33B15, 33B99, 34A25

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.

Keywords

vertices, edges, faces, Planar graph, disconnected graph, intuitive analysis