ALGORITHM FOR CONSTRUCTING THE TRIPLE UNIT GRAPH OF TYPE II OF RING ℤn USING PYTHON

Abstract

Let R be a commutative ring with U(R) as the set of all unit elements in R. This paper introduces a new graph associated with the ring R, called the triple unit graph of type II, denoted by TU2(R) with the vertex set is R − {0,1}. In TU2(R), two distinct vertices, uand v, are adjacent if there exists w ∈ R − {0,1} with w ≠ u and w ≠ v such that uvw ∈ U(R). This paper focuses on the algorithm for constructing TU2(ℤn) using Python. This research uses the literature study research method. The Python programming language can be used to observe the characteristic result of the graph. From the patterns generated by the algorithm, some characteristics of TU2(ℤn) are obtained. For example, if n is a prime and n ≥ 5, then TU2(ℤn) is a connected graph, a complete graph, a regular graph, and a Hamiltonian graph.