Numerical Invariants of Coprime Graph of A Generalized Quaternion Group

Nurhabibah Nurhabibah (Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram)
I Gede Adhitya Wisnu Wardhana (University of Mataram)
Ni Wayan Switrayni (Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram)

Journal of the Indonesian Mathematical Society
VOLUME 29 NUMBER 1 (MARCH 2023)

The coprime graph of a finite group was defined by Ma, denoted by ΓG, is a graph with vertices that are all elements of group G and two distinct vertices x and y are adjacent if and only if (|x|, |y|) = 1. In this study, we discuss numerical invariants of a generalized quaternion group. The numerical invariant is a property of a graph in numerical value and that value is always the same on an isomorphic graph. This research is fundamental research and analysis based on patterns in some examples. Some results of this research are the independence number of ΓQ4n is 4n − 1 or 3n and its complement metric dimension is 4n − 2 for each n ≥ 2.