Explanipedia

Bounds of Geodetic-Wiener Index on Spirocyclic Graphs Open

Rosalio Artes, R. U. Gobithaasan, Roslan Hasni, Nader Jafari Rad · 2025

Wiener index has been extensively studied for several decades because of its applications in chemistry. Many variants of Wiener index were defined and their corresponding bounds were explored. In this work, we introduced the concept of geo…

Sharp Lower Bound for Randić index of Trees with Fixed Roman Domination Number Open

Fateme Movahedi, Mohammad Hadi Akhbari, Roslan Hasni · 2024

Let be a simple connected graph with vertex set and edge set . The Randić index of graph is the value , where and refer to the degree of the vertices and . We obtain a lower bound for the Randić index of trees in terms of the order and the…

Computing the Hosoya Index of Some Nanostar Dendrimers Open

Fateme Movahedi, Mohamad Hadi Akhbari, Roslan Hasni · 2024

Dendrimers are highly branched macromolecules built up from a monomer, with new branches added in steps until a tree structure is created. The various biological characteristics of dendrimers are a good choice in chemistry, biology, the me…

Domination (totally) Dot-critical of Harary Graphs Open

Roslan Hasni, Doost Ali Mojdeh, Suraya Abu Bakar · 2024

A graph G is referred to as domination vertex critical if the removal of any vertex results in a reduction of the domination number. It is considered dot-critical (or totally dot-critical) if contracting any edge (or identifying any two ve…

Novel Concepts on Domination in Neutrosophic Incidence Graphs with Some Applications Open

Siti Nurul Fitriah Mohamad, Roslan Hasni, Florentín Smarandache · 2023

In graph theory, the concept of domination is essential in a variety of domains. It has broad applications in diverse fields such as coding theory, computer network models, and school bus routing and facility location problems. If a fuzzy …

Circular q-Rung Orthopair Fuzzy Set and Its Algebraic Properties Open

Binyamin Yusoff, Adem Kılıçman, Dian Pratama, Roslan Hasni · 2023

Circular intuitionistic fuzzy sets (CIFS) are a recent extension of intuitionistic fuzzy sets (IFS) that can handle imprecise membership values effectively. However, its representation is limited to the space under the intuitionistic fuzzy…

On Dominating Energy in Bipolar Single-Valued Neutrosophic Graph Open

Siti Nurul Fitriah Mohamad, Roslan Hasni, Binyamin Yusoff · 2023

One of the most important concepts in graph theory for dealing with unpredictable phenomena is the concept of domination and it has gained attention from many scholars. Recently, dominating energy of graph plays a vital role in the field o…

Maximum Second Zagreb Index Of Trees With Given Roman Domination Number Open

Ayu Ameliatul Ahmad Jamri, Roslan Hasni, Muhammad Kamran Jamil, Doost Ali Mojdeh · 2023

Chemical study regarding total $\\pi$-electron energy with respect to conjugated molecules has focused on the second Zagreb index of graphs. Moreover, in the last half-century, it has gotten a lot of attention. The relationship between the…

Atom-Bond Connectivity and Geometric Arithmetic Indices of Dendrimer Nanostars Open

N. M. Husin, Roslan Hasni, Nabeel E. Arif · 2023

Let G be a molecular graph. The atom-bond connectivity (ABC) and geometric-arithmetic (GA) indices of G are defined as and , where (or ) denoted the degree of the vertex u (or v), respectively. A dendrimer is a hyperbranched molecule built…

Minimum Randić Index of Trees with Fixed Total Domination Number Open

Ayu Ameliatul Shahilah Ahmad Jamri, Fateme Movahedi, Roslan Hasni, R. U. Gobithaasan, Mohammad Hadi Akhbari · 2022

The Randić index is among the most famous degree-based topological indices in chemical graph theory. It was introduced due to its application in modeling the properties of certain molecular structures and has been extensively studied. In t…

A REMARK ON THE EDGE IRREGULARITY STRENGTH OF CORONA PRODUCT OF TWO PATHS Open

Roslan Hasni, I. Tarawneh, Mohamad Nazri Husin · 2022

With respect to a simple graph G, a vertex labeling ϕ: V(G) > {1,2,...,k) is known as k-labeling. The weight corresponding to an edge xy in G, expressed as wϕ (xy), represents the labels sum of end vertices x and y, given by wϕ (xy) = ϕ(x)…

4-total edge product cordial for some star related graphs Open

Almothana Azaizeh, Roslan Hasni, Firas Haddad, Mutasem K. Alsmadi, Raed Alkhasawneh , et al. · 2022

Let G = (V (G), E(G)) be a graph, define an edge labeling function ψ from E(G) to {0, 1, . . . , k − 1} where k is an integer, 2 ≤ k ≤ |E(G)|, induces a vertex labeling function ψ∗ from V (G) to {0, 1, . . . , k − 1} such that ψ∗(v) = ψ(e1…

Edge Irregular Reflexive Labeling for Some Classes of Plane Graphs Open

Yoong Kooi Kuan, Roslan Hasni, Lau G. C., Muhammad Irfan · 2022

For a graph G, we define a total k-labeling ϕ as a combination of an edge labeling ϕe(x) → {1, 2, . . . , ke} and a vertex labeling ϕv(x) → {0, 2, . . . , 2kv}, such that ϕ(x) = ϕv(x) if x ∈ V (G) and ϕ(x) = ϕe(x) if x ∈ E(G), where k = ma…

Reflexive edge strength of convex polytopes and corona product of cycle with path Open

Yoong Kooi Kuan, Roslan Hasni, Gee-Choon Lau, Muhammad Ahsan Asim, Ali Ahmad · 2022

For a graph $ G $, we define a total $ k $-labeling $ \varphi $ is a combination of an edge labeling $ \varphi_e(x)\to\{1, 2, \ldots, k_e\} $ and a vertex labeling $ \varphi_v(x) \to \{0, 2, \ldots, 2k_v\} $, such that $ \varphi(x) = \varp…

Maximal first Zagreb index of trees with given Roman domination number Open

Zhibin Du, Ayu Ameliatul Shahilah Ahmad Jamri, Roslan Hasni, Doost Ali Mojdeh · 2022

The first Zagreb index of graphs is defined to be the sum of squares of degrees of all the vertices of graphs. It drew a great deal of attention in the past half-century. In this paper, we study the relationship between the first Zagreb in…

PERSONAL SHARING IN SOCIAL NETWORK ANALYSIS – A CASE STUDY IN UNIVERSITI MALAYSIA TERENGGANU Open

Roslan Hasni, NURUL ATIQAH MOHD RADZI, Mohamad Nazri Husin · 2021

In this paper, we discuss a case-study of personal sharing of information among students of two undergraduate programme, i.e., Computational Mathematics and Software Engineering (in short, CM and SE respectively) at UniversitiMalaysia Tere…

On the Zagreb indices of graphs with given Roman domination number Open

Ayu Ameliatul Shahilah Ahmad Jamri, Roslan Hasni, Sharifah Kartini Said Husain · 2021

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. The two Zagreb indices $M_1=sum_{vin V(G)} d^2_G(v)$ and $M_2=sum_{uvin E(G)} d_G(u)d_G(v)$ are vertex degree based graph invariants that have been introduced in the 1970s and …

Analysis of Distance-Based Topological Polynomials Associated with Zero-Divisor Graphs Open

Ali Ahmad, Roslan Hasni, Nahid Akhter, Kashif Elahi · 2021

Chemical compounds are modeled as graphs. The atoms of molecules represent the graph vertices while chemical bonds between the atoms express the edges. The topological indices representing the molecular graph corresponds to the different c…

Novel Concept of Energy in Bipolar Single-Valued Neutrosophic Graphs with Applications Open

Siti Nurul Fitriah Mohamad, Roslan Hasni, Florentín Smarandache, Binyamin Yusoff · 2021

The energy of a graph is defined as the sum of the absolute values of its eigenvalues. Recently, there has been a lot of interest in graph energy research. Previous literature has suggested integrating energy, Laplacian energy, and signles…

On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes Open

Sakander Hayat, Muhammad Yasir Hayat Malik, Ali Ahmad, Suliman Khan, Faisal Yousafzai , et al. · 2021

A convex polytope is the convex hull of a finite set of points in the Euclidean space ℝ n . By preserving the adjacency-incidence relation between vertices of a polytope, its structural graph is constructed. A graph is called Hamil…

Novel Concept of Interval-ValuedNeutrosophic Incidence Graphswith Application Open

Siti Nurul Fitriah Mohamad, Roslan Hasni, Naeem Jan, Muhammad Jamil · 2021

Neutrosophic set (NS) is a framework used when the imprecision and uncertainty of an event aredescribed based on three possible aspects,i.e.,the membership degree, neutral membership degreeand non-membership degree. On the other hand, neut…

Novel Concept of Interval-Valued Neutrosophic Incidence Graphs with Application Open

Siti Nurul Fitriah Mohamad, Roslan Hasni, Binyamin Yusoff, Naeem Jan, Muhammad Jamil · 2021

Neutrosophic set (NS) is a framework used when the imprecision and uncertainty of an event are described based on three possible aspects, i.e., the membership degree, neutral membership degree and non-membership degree. On the other hand, …

Bounds of Degree-Based Molecular Descriptors for Generalized F -sum Graphs Open

Jia Liu, Sana Akram, Muhammad Javaid, Abdul Raheem, Roslan Hasni · 2021

A molecular descriptor is a mathematical measure that associates a molecular graph with some real numbers and predicts the various biological, chemical, and structural properties of the underlying molecular graph. Wiener (1947) and Trinjas…

On the edge irregular reflexive labeling of corona product of graphs with path Open

Yoong Kooi Kuan, Roslan Hasni, Muhammad Irfan, Ibrahim Taraweh, Ali Ahmad , et al. · 2021

We define a total k-labeling (Formula presented.) of a graph G as a combination of an edge labeling (Formula presented.) and a vertex labeling (Formula presented.) such that (Formula presented.) if (Formula presented.) and (Formula present…

On the edge irregularity strength for some classes of plane graphs Open

I. Tarawneh, Roslan Hasni, Ali Ahmad, Muhammad Ahsan Asim · 2021

Graph labeling is an assignment of (usually) positive integers to elements of a graph (vertices and/or edges) satisfying certain condition(s). In the last two decades, graph labeling research received much attention from researchers. This …

Irregularity Strength of Circulant Graphs Using Algorithmic Approach Open

Muhammad Ahsan Asim, Roslan Hasni, Ali Ahmad, Basem Assiri, Andrea Semaničová–Feňovčíková · 2021

This paper deals with decomposition of complete graphs on vertices into circulant graphs with reduced degree . They are denoted as , where to are generators. Mathematical labeling for such bigger (higher order and huge size) and complex…

On the first general Zagreb eccentricity index Open

Muhammad Kamran Jamil, Muhammad Imran, Aisha Javed, Roslan Hasni · 2020

In a graph G, the distance between two vertices is the length of the shortest path between them. The maximum distance between a vertex to any other vertex is considered as the eccentricity of the vertex. In this paper, we introduce …

Extremal Trees with Respect to the Difference between Atom-Bond Connectivity Index and Randić Index Open

Wan Nor Nabila Nadia Wan Zuki, Zhibin Du, Muhammad Kamran Jamil, Roslan Hasni · 2020

Let G be a simple, connected and undirected graph. The atom-bond connectivity index (ABC(G)) and Randić index (R(G)) are the two most well known topological indices. Recently, Ali and Du (2017) introduced the difference between atom-bond c…

On topological aspects of bilayer Germanium Phosphide Open

Farukh Ejaz, Muhammad Tanveer Hussain, Roslan Hasni · 2020

A material having electrical conductivity value falling between conductor and insulator is known as semiconductor.Due to high adaptability of these materials makes them best basic material used in advanced electronics and communications.So…

Spectral Properties with the Difference between Topological Indices in Graphs Open

Akbar Jahanbani, Roslan Hasni, Zhibin Du, Seyed Mahmoud Sheikholeslami · 2020

Let be a graph of order with vertices labeled as . Let be the degree of the vertex , for . The difference adjacency matrix of is the square matrix of order whose entry is equal to if the vertices and of are adjacent or and zero …

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