Document Type : Regular Article

Authors

• Ola A. Neamah
• Shatha A. Salman

Mathematics and Computer Application, Department Applied Sciences, University of Technology – Iraq

Abstract

Graph Theory is a discipline of mathematics with numerous outstanding issues and applications in various sectors of mathematics and science. The chromatic polynomial is a type of polynomial that has valuable and attractive qualities. Ehrhart's polynomials and chromatic analysis are two essential techniques for graph analysis. They both provide insight into the graph's structure but in different ways. The relationship between chromatic and Ehrhart polynomials is an area of active research that has implications for graph theory, combinatorial, and other fields. By understanding the relationship between these two polynomials, one can better understand the structure of graphs and how they interact. This can help us to solve complex problems in our lives more efficiently and effectively. This work gives the relationship between these two essential polynomials and the proof of theorems, and an application related to these works, the model Physical Cell ID (PCID), was discussed.

Keywords

• Chromatic polynomial
• Ehrhart polynomial
• h^*-polynomial
• Symmetric polynomials

Main Subjects

• Applied Mathematics