Akmal Bachtiar Ismail Huda, Hery Susanto, Mohammad Agung
Letfl be a ring. The set of nilpotent elements of R is denoted by Nil(R). The nilpotent graph of R is denoted by G(R), that is the graph with element R\Nil(R) as the vertex set such that two distinct vertices are adjacent if sum of two vertices is element Nil(R). Let r2(Zn) be a 2 x 2 upper triangular matrix ring over integer modulo n. In this article, we will discuss about nilpotent graph of T2(l,p) and T2{TL2^) where p is a prime number greater than or equal to 3. The research method used in this research is the literature study method. The result of this research show that the general form of G (T2 (Zp)) is graph having disjoint complete bipartite subgraphs and the general form of G (T2 (Z2p)) is graph having disjoint complete subgraphs and disjoint complete bipartite subgraphs. Furthermore, we use these result to investigate girth, clique number, diameter, and dominating number. © 2025 American Institute of Physics Inc.. All rights reserved.
Department of Mathematics, Universitas Negeri Malang, Malang, Indonesia
