The Distinguishing Chromatic Number

Different Families of Graphs

Presenter: Salvador Ochoa Zavalza

Presenter Status: Undergraduate student

Academic Year: 22-23

Semester: Spring

Faculty Mentor: Izabela Kanaana

Department: Mathematics

Funding Source/Sponsor: McNair

Screenshot URL: https://drive.google.com/uc?id=1ZKzXdqBQnHErNLJTSE_0EcZjOp2QvbK0

Abstract:
The distinguishing chromatic number of a graph χD (G) is the number that gives us the Chromatic number of a graph after all permutations are considered. However, calculating this number is not as straightforward as it may seem; in other words, no closed form formula has been determined to calculate χD (G). In this poster we study the need for a distinguishing chromatic number in a real world scenario and give the distinguishing chromatic number of some families of graphs such as the wheel graph Wn, rectangular grids graphs G(n,m), platonic solids, and some snarks.