The Intersection Graph Representation of a Dihedral Group With Prime Order and Its Numerical Invariants

Ramdani, Dewi Santri; Wardhana, I Gede Adhitya Wisnu; Awanis, Zatta Yumni

doi:10.30598/barekengvol16iss3pp1013-1020

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…Beberapa peneliti telah membahas mengenai indeks topologi pada graf, salah satunya adalah Husni dkk [6] yang telah membahas mengenai indeks Harmonik dan indeks Gutman pada graf coprima dari grup modulo dengan orde pangkat prima, kemudian Asmarani dkk [1] mengangkat kasus indeks Zagreb, indeks Weiner dan indeks Harmonik pada graf pangkat atas grup dihedral, dan Putra dkk [10] juga membahas mengenai indeks topologi dari graf pangkat pada grup bilangan bulat modulo, serta Ismail yang memberikan formulasi indeks Zagreb dari graf pembagi nol [11]. Penelitian ini khusus difokuskan pada indeks topologi Szeged dan indeks topologi Padmakar-Ivan (PI) pada graf nilpoten yang telah dijelaskan sebelumnya.…”

Section: Pendahuluanunclassified

“…Sehingga didapatkann index Padmakar-Ivan (PI) sebagai berikut ; Teorema 3.4 dan Teorema 3.5 pada studi ini, secara khusus melengkapi hasil karakterisasi oleh Malik dan koleganya (Malik et al, 2023). Sekaligus juga memperkaya formulasi indeks topologi lain yang telah diberikan oleh beberapa penulis pada representasi graf yang berbeda dan dari struktur aljabar yang berbeda, diantaranya indeks Zagreb, indeks Harmonic, indeks Gutman, hingga indeks Weiner (Asmarani et al, 2023;Husni et al, 2022;Putra et al, 2023;Semil @ Ismail et al, 2023). Formulasi indeks Szeged dan indeks Padmakar-Ivan dalam penelitian ini diharapkan dapat memberikan pandangan baru mengenai ukuran numerik dari hubungan antar elemen-elemen dalam gelanggang, terutama dalam konteks hubungannya dengan unsur-unsur nilpoten.…”

Section: Buktiunclassified

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Szeged Index and Padmakar-Ivan Index of Nilpotent Graph of Integer Modulo Ring with Prime Power Order

Husni,

Wardhana,

Dewi

et al. 2023

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Recently, graphs have started to be used to represent a finite ring. Nikmehr and Khojasteh in the article defined the nilpotent graph of a ring . Denoted , is a graph with the set of vertices being all the elements in the ring Two vertices and are adjacent if and only if is nilpotent elements in the ring . Topological index is a field that discusses graph structure based on the degree of each vertex of a graph and the distance between vertices. In this study, the author will gives the general formula of the Szeged index and Padmakar-Ivan index of the nilpotent graph graph of the modulo ring with prime power order. The result of this research is a general formula for the topological indices of nilpotent graphs of the integer modulo ring, called the Szeged index and the Padmakar-Ivan index.

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Section: Pendahuluanunclassified

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Szeged Index and Padmakar-Ivan Index of Nilpotent Graph of Integer Modulo Ring with Prime Power Order

Husni,

Wardhana,

Dewi

et al. 2023

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“…During the quarantine period, there are two possibilities that will happen to COVID-19 patients: patients will recover, or the worst possibility will die. Based on this explanation, the more appropriate model used to describe the state of COVID-19 is to use the SIQRD model [4], [11]- [14].…”

Section: Introductionmentioning

confidence: 99%

Model of Transmission Covid-19 Using Siqrd Model With the Effect of Vaccination in Mataram

Febryantika,

Marwan,

Awalushaumi

et al. 2023

BAREKENG: J. Math. & App.

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Mathematical modeling is considered an effective tool for analyzing real-life problems. In this research, we analyze the dynamics of the COVID-19 spread in Mataram city using the SIQRD model with influence of the vaccination. The analyze based on varying some parameter values of the model i.e the transmission rate (β), the recovery rate for COVID-19 (γ), and the death rate (δ), before and after vaccination respectively. Our chosen methodology involves parameter estimation using the Euler method. The result shows that the model has an endemic equilibrium point which remains stable before and after vaccination. Furthermore, the basic reproduction number (R0) which states the number of secondary cases that occur if there are infected people in a population, has the value more than 1 before the vaccination, but equal to 1 after the vaccination. This suggests that prior to COVID-19 vaccination, infected individuals could potentially infect more than one person, but after vaccination, each infected person tends to only infect one other individual. This shift is attributed to the subsidence of COVID-19 symptoms following vaccination

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The Chemical Topological Graph Associated With the Nilpotent Graph of a Modulo Ring of Prime Power Order

Malik,

Husni,

Miftahurrahman

et al. 2024

JFMA

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Chemical topological graph theory constitutes a subdomain within mathematical chemistry that leverages graph theory to model chemical molecules. In this context, a chemical graph serves as a graphical representation of molecular structures. Specifically, a chemical molecule is portrayed as a graph wherein atoms are denoted as vertices, and the interatomic bonds are represented as edges within the graph. Various molecular properties are intricately linked to the topological indices of these molecular graphs. Notably, commonly employed indices encompass the Wiener Index, the Gutman Index, and the Zagreb Index. This study is directed towards elucidating the numerical invariance and topological indices inherent to a nilpotent graph originating from a modulo integer ring with prime order. Consequently, the investigation seeks to discern how the Wiener Index, the Zagreb Index, and other characteristics of the nilpotent graph manifest within a ring of integers modulo prime order powers.

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The Intersection Graph Representation of a Dihedral Group With Prime Order and Its Numerical Invariants

Cited by 3 publications

References 9 publications

Szeged Index and Padmakar-Ivan Index of Nilpotent Graph of Integer Modulo Ring with Prime Power Order

Szeged Index and Padmakar-Ivan Index of Nilpotent Graph of Integer Modulo Ring with Prime Power Order

Model of Transmission Covid-19 Using Siqrd Model With the Effect of Vaccination in Mataram

The Chemical Topological Graph Associated With the Nilpotent Graph of a Modulo Ring of Prime Power Order

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