The Clique Number and The Chromatics  Number Of The Coprime Graph for The Generalized Quarternion Group

Marena Rahayu Gayatri; Nurhabibah Nurhabibah; Qurratul Aini; Zata Yumni Awanis; Salwa Salwa; I Gede Adhitya Wisnu Wardhana

doi:10.31764/jtam.v7i2.13099

The Clique Number and The Chromatics Number Of The Coprime Graph for The Generalized Quarternion Group

Marena Rahayu Gayatri, Nurhabibah Nurhabibah, Qurratul Aini, Zata Yumni Awanis, Salwa Salwa, I Gede Adhitya Wisnu Wardhana

Abstract

Graph theory can give a representation of abstract mathematical systems such as groups or rings. We have many graph representations for a group, in this study we use the coprime graph representation for a generalized quaternion group to find the numerical invariants of the graph, which are the clique number and the chromatic number. The main results obtained from this study are the clique number of the coprime graph representation for the generalized quaternion group is equal to the chromatic number of the coprime graph representation for the generalized quaternion group for each case of the order.

Keywords

Clique number; Chromatic number; Coprime graph; Generalized quaternion group.

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References

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DOI: https://doi.org/10.31764/jtam.v7i2.13099