arXiv subjects

Nor Haniza Sarmin

Publications and source records attributed to Nor Haniza Sarmin.

4 recordsLinked to original sources

arXiv2026

The Diametral Metric Dimension of Generalized Corona Graph

This study investigates the diametral metric dimension of generalized corona graphs, where the main graph is connected graph and the branch graphs form a sequence of connected graphs. The concept of diametral metric dimension is an extension of the metric dimension concept, requiring the resolving set to contain all diametral vertices. To determine the diametral metric dimension of a generalized corona graph, one must first identify the distance of each vertex in the graph and the graph's diametral set. Subsequently, a resolving set containing the diametral set is determined. The results show that the diametral metric dimension of the generalized corona graph depends on the diameter of the main graph and the metric dimensions of the graphs in the sequence. These concepts provide theoretical insights into resolving structures in the planning infrastructure and motivate further studies on other graph families and graph operations.

math.CO↗

arXiv2021

Unity Product Graph of Some Commutative Rings

A graph is an instrument which is extensively utilized to model various problems in different fields. Up to date, many graphs have been developed to represent algebraic structures, particularly rings in order to study their properties. In this article, by focusing on commutative ring $ R $, we introduce a new notion of unity product graph associated with $ R $ and its complement. In addition, we prove that if the number of vertices of the unity product graph is at least 2, then the graph is disconnected, while its complement graph is connected. Furthermore, it is shown that there are some commutative rings with such as Boolean ring and the Cartesian product of Boolean rings in which their associated unity product graphs are trivial. Consequently, some results are established to determine the number of isolated vertices in unity product graph. We also characterize commutative rings with unity in which their associated unity product and complement unity product graphs are empty graph and complete graph, respectively. Finally, we prove some results on the properties of the unity product graph and its complement in terms of girth, diameter, radius, dominating number, chromatic number and clique number as well as planarity and Hamiltonian.

math.CO↗

arXiv2020

On the Non-Commuting Graph of the Group $U_{6n}$

A non-commuting graph of a finite group $G$ is a graph whose vertices are non-central elements of $G$ and two vertices are adjacent if they don't commute in $G$. In this paper, we study the non-commuting graph of the group $U_{6n}$ and explore some of its properties including the independent number, clique and chromatic numbers. Also, the general formula of the resolving polynomial of the non-commuting graph of the group $U_{6n}$ are provided. Furthermore, we find the detour index, eccentric connectivity, total eccentricity and independent polynomials of the graph.

math.CO↗

arXiv2012

Some considerations on the nonabelian tensor square of crystallographic groups

The nonabelian tensor square $G\otimes G$ of a polycyclic group $G$ is a polycyclic group and its structure arouses interest in many contexts. The same assertion is still true for wider classes of solvable groups. This motivated us to work on two levels in the present paper: on a hand, we investigate the growth of the Hirsch length of $G\otimes G$ by looking at that of $G$, on another hand, we study the nonabelian tensor product of pro--$p$--groups of finite coclass, which are a remarkable class of solvable groups without center, and then we do considerations on their Hirsch length. Among other results, restrictions on the Schur multiplier will be discussed.

math.GR↗