THE NON-COPRIME GRAPHS OF UPPER UNITRIANGULAR MATRIX GROUPS OVER THE RING OF INTEGER MODULO WITH PRIME ORDER AND THEIR TOPOLOGICAL INDICES

DOI: https://doi.org/10.30598/barekengvol19iss1pp547-556
Keywords: Non-Coprime Graphs, The Upper Unitriangular Matrix Group, Harmonic Index, Wiener Index, Harary Index, First Zagreb Index

Abstract

In its application graph theory is widely applied in various fields of science, including scheduling, transportation, industry, and structural chemistry, such as topological indexes. The study of graph theory is also widely applied as a form of representation of algebraic structures, including groups. One form of graph representation that has been studied is non-coprime graphs. The upper unitriangular matrix group is a form of group that can be represented in graph form. This group consists of upper unitriangular matrices, which are a special form of upper triangular matrix with entries in a ring R and all main diagonal entries have a value of one. In this research, we look for the form of a non-coprime graph from the upper unitriangular matrix group over a ring of prime modulo integers and several topological indexes, namely the Harmonic index, Wiener index, Harary index, and First Zagreb index. The findings of this research indicate that the structure of the graph and the general formula for the Harmonic index, Wiener index, Harary index, and First Zagreb index were successfully obtained.

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Published
2025-01-13
How to Cite
[1]
M. Afdhaluzzikri, I. G. A. W. Wardhana, F. Maulana, and H. R. Biswas, “THE NON-COPRIME GRAPHS OF UPPER UNITRIANGULAR MATRIX GROUPS OVER THE RING OF INTEGER MODULO WITH PRIME ORDER AND THEIR TOPOLOGICAL INDICES”, BAREKENG: J. Math. & App., vol. 19, no. 1, pp. 547-556, Jan. 2025.
Issue
Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
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Articles

Copyright (c) 2025 M. Afdhaluzzikri, I Gede Adhitya Wisnu Wardhana, Fariz Maulana, Hena Rani Biswas

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