Hasmawati Basir - Academia.edu (original) (raw)

Papers by Hasmawati Basir

Research paper thumbnail of Total edge irregularity strength of subdivision of star

Journal of Discrete Mathematical Sciences and Cryptography, Nov 2, 2015

Abstract This research is the development from Siddiqui's research on edge irregularity stren... more Abstract This research is the development from Siddiqui's research on edge irregularity strength of subdivision of star. Siddiqui [3] had determined the total edge irregularity strength of sub-division of star S m for 1≤m≤8 and n≥3. However, the total edge of irregularity strength for star subdivision S m for m≥9 and n≥3 are still in an open problem and also the total edge irregularity strength of subdivision of star by inserting mi vertices on different to every edge of a star Sn yet to be determined.In this paper, it will be proven that the total edge irregularity strength of subdivision of star S m for m≥9 and n≥3 and the total edge irregularity strength of subdivision of star Snm1, m2, ⋯ ,mn for mi≥1, mi

Research paper thumbnail of Ramsey Number on A Union of Stars Versus A Small Cycle

Jurnal Matematika, Statistika dan Komputasi, Mar 17, 2018

The Ramsey number for a graph versus a graph , denoted by , is the smallest positive integer such... more The Ramsey number for a graph versus a graph , denoted by , is the smallest positive integer such that for any graph of order , either contains as a subgraph or ̅ contains as a subgraph. In this paper, we investigate the Ramsey numbers for stars versus small cycle. We show that and for and .

Research paper thumbnail of Total H-irregularity strength of ladder graphs

Journal of physics, May 1, 2019

Specifying parameters for a model is often a problem confronted by the developer of a game or sim... more Specifying parameters for a model is often a problem confronted by the developer of a game or simulation. It is often something which comes up after the basic relationships have been defined and coded. This paper presents the results of a survey which sought to establish some of the important parameters of a physical distribution system.

Research paper thumbnail of Bilangan Stirling dan Hubungannya dengan Beberapa Konsep Matematika

Jurnal Matematika, Statistika dan Komputasi, Feb 1, 2018

Dalam tulisan ini dibahas analogi, ekuivalensi dan keterkaitan antara bilangan-bilangan Stirling ... more Dalam tulisan ini dibahas analogi, ekuivalensi dan keterkaitan antara bilangan-bilangan Stirling dengan konsep matematika yang lain: himpunan, permutasi, fungsi, faktorial (turun dan naik), determinan-1 dan deret Maclaurin. Pada khususnya analogi antara diferensi dan turunan bisa diturunkan dengan menggunakan bilangan-bilangan Stirling. Juga ekuivalensi beberapa definisi bilangan Stirling berdasarkan konsep partisi pada permutasi dan pada himpunan serta interpretasinya, juga disajikan. Pada penerapan konsep determinan-1, diberikan dua relasi rekurensi yang berbeda tetapi ekuivalen. Relasi rekurensi yang pertama menghasilkan sebuah barisan eigen sedangkan relasi rekurensi yang kedua menghasilkan barisan eigen yang sama, tetapi diturunkan dengan menerapkan determinan-1. Kata Kunci : bilangan Stirling jenis pertama dan kedua, faktorial turun, partisi, relasi rekurensi, determinan-1.

Research paper thumbnail of Analisis Penyelesaian Persamaan Kuadrat Matriks

Jurnal Matematika, Statistika dan Komputasi, Feb 4, 2018

Persamaan kuadrat matriks dalam matriks n x n muncul dalam dunia aplikasi dan merupakan salah sat... more Persamaan kuadrat matriks dalam matriks n x n muncul dalam dunia aplikasi dan merupakan salah satu persamaan matriks nonlinier yang paling sederhana. Kita memberikan karakterisasi lengkap dari penyelesaian dalam bentuk generalisasi dekomposisi Schur. Beberapa variasi dari teknik penyelesaian numerik juga disajikan.

Research paper thumbnail of Modular Irregular Labeling On Complete Graphs

Daya Matematis: Jurnal Inovasi Pendidikan Matematika

Let G be a simple graph of n order. An edge labeling such that the weights of all vertex are diff... more Let G be a simple graph of n order. An edge labeling such that the weights of all vertex are different and elements of the set modulo n, are called a modular irregular labeling. The modular irregularity strength of G is a minimum positive integer k such that G have a modular irregular labeling. If the modular irregularity strength is none, then we called the modular irregularity strength of G is infinity. In this article, we determine the modular irregularity strength of complete graphs.

Research paper thumbnail of Pelabelan Total Tidak Teratur Titik Graf Unidentified Flying Object

Jurnal Kajian Matematika dan Aplikasinya (JKMA), Jul 31, 2022

For a graph G that have vertex set and edge set. A labelling : ∪ → {1,2,3, … , } is called a vert... more For a graph G that have vertex set and edge set. A labelling : ∪ → {1,2,3, … , } is called a vertex irregularity total k-labeling of if for any two different vertices and in have () ≠ () where () = () + ∑ () ∈ (). The smallest positive integer such that has a vertex irregular total k-labeling is called the total vertex irregularity strength of , denoted by (). In this paper, we determined the total vertex irregularity strength of Unidentified Flying Object Graph, (,). The result in this paper as follows:

Research paper thumbnail of Analisis Penyelesaian Persamaan Kuadrat Matriks

Jurnal Matematika, Statistika dan Komputasi, Feb 4, 2018

Persamaan kuadrat matriks dalam matriks n x n muncul dalam dunia aplikasi dan merupakan salah sat... more Persamaan kuadrat matriks dalam matriks n x n muncul dalam dunia aplikasi dan merupakan salah satu persamaan matriks nonlinier yang paling sederhana. Kita memberikan karakterisasi lengkap dari penyelesaian dalam bentuk generalisasi dekomposisi Schur. Beberapa variasi dari teknik penyelesaian numerik juga disajikan.

Research paper thumbnail of Bilangan Stirling dan Hubungannya dengan Beberapa Konsep Matematika

Dalam tulisan ini dibahas analogi, ekuivalensi dan keterkaitan antara bilangan-bilangan Stirling ... more Dalam tulisan ini dibahas analogi, ekuivalensi dan keterkaitan antara bilangan-bilangan Stirling dengan konsep matematika yang lain: himpunan, permutasi, fungsi, faktorial (turun dan naik), determinan-1 dan deret Maclaurin. Pada khususnya analogi antara diferensi dan turunan bisa diturunkan dengan menggunakan bilangan-bilangan Stirling. Juga ekuivalensi beberapa definisi bilangan Stirling berdasarkan konsep partisi pada permutasi dan pada himpunan serta interpretasinya, juga disajikan. Pada penerapan konsep determinan-1, diberikan dua relasi rekurensi yang berbeda tetapi ekuivalen. Relasi rekurensi yang pertama menghasilkan sebuah barisan eigen sedangkan relasi rekurensi yang kedua menghasilkan barisan eigen yang sama, tetapi diturunkan dengan menerapkan determinan-1.

Research paper thumbnail of On irregularity strength of diamond network

AKCE International Journal of Graphs and Combinatorics, 2018

In this paper we investigate the total edge irregularity strength tes(G) and the total vertex irr... more In this paper we investigate the total edge irregularity strength tes(G) and the total vertex irregularity strength tvs(G) of diamond graphs Br n and prove that tes(Br n) = ⌈(5n − 3)/3⌉, while tvs(Br n) = ⌈(n + 1)/3⌉.

Research paper thumbnail of Total H-irregularity strength of ladder graphs

Journal of Physics: Conference Series, 2019

H-irregular total labeling and total H-irregularity strength of graphs were not complete.This res... more H-irregular total labeling and total H-irregularity strength of graphs were not complete.This research aimed to determine the total H-Irregularity strength of ladder graph Lb with subgraphs C 8 and C 10.To determine of the total H-irregularity strength of ladder graphs, we have to determine the greatest lower bound and the smallest upper bound. The lower bound was analysed based on graph characteristics and other supporting theorems, while the upper bound was analysed by construct a function H-Irregular total labeling. The results reveal that the total H-Irregularity strength of ladder graph Ln with subgraph C 8 is ⌈ n − 2 i + 14 16 ⌉ ≤ t h s ( L n , C 8 ) ≤ ⌈ n + 14 18 ⌉ , for 18 i − 15 ≤ n ≤ 18 i + 2 , where i = 1,2, …, N and the total H-Irregularity strength of ladder graph Ln with subgraph C 10 is t h s ( G , H ) ≥ max { ⌈ 1 + m 1 − 1 | V ( H / S 1 ) | + | E ( H / S 1 ) | ⌉ , … , ⌈ 1 + m 1 − 1 | V ( H / S z ) | + | E ( H / S z ) | ⌉ } ⌈ n − 3 i + 18 20 ⌉ ≤ t h s ( L n , C 10 ) ≤...

Research paper thumbnail of Total edge irregularity strength of subdivision of star

Journal of Discrete Mathematical Sciences and Cryptography, 2015

Research paper thumbnail of Ramsey Number on A Union of Stars Versus A Small Cycle

The Ramsey number for a graph versus a graph , denoted by , is the smallest positive integer such... more The Ramsey number for a graph versus a graph , denoted by , is the smallest positive integer such that for any graph of order , either contains as a subgraph or ̅ contains as a subgraph. In this paper, we investigate the Ramsey numbers for stars versus small cycle. We show that and for and .

Research paper thumbnail of Pelabelan Total Tidak Teratur Titik Graf Unidentified Flying Object

Jurnal Kajian Matematika dan Aplikasinya (JKMA), Jul 31, 2022

For a graph G that have vertex set V and edge set E. A labelling f:VUE->{1,2,3,...,k} is called a... more For a graph G that have vertex set V and edge set E. A labelling f:VUE->{1,2,3,...,k} is called a vertex irregularity total k-labeling of G if for any two different vertices x and y in V have wt(x)\neq wt(y) where wt(x)=f(x)+∑_{yV(G)} f(xy). The smallest positive integer k such that G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G , denoted by tvs(G).

In this paper, we determined the total vertex irregularity strength of Unidentified Flying Object Graph, tvs(U_(m,n}). The result in this paper as follows:

tvs(U_{m,n})=(3n+1)/2 for 3<=m<=3((n+1)/2), n>=3, and

tvs(U_{m,n})=(3n+m)/3 for m>3((n+1)/2), n>=3.

Research paper thumbnail of Total edge irregularity strength of subdivision of star

Journal of Discrete Mathematical Sciences and Cryptography, Nov 2, 2015

Abstract This research is the development from Siddiqui's research on edge irregularity stren... more Abstract This research is the development from Siddiqui's research on edge irregularity strength of subdivision of star. Siddiqui [3] had determined the total edge irregularity strength of sub-division of star S m for 1≤m≤8 and n≥3. However, the total edge of irregularity strength for star subdivision S m for m≥9 and n≥3 are still in an open problem and also the total edge irregularity strength of subdivision of star by inserting mi vertices on different to every edge of a star Sn yet to be determined.In this paper, it will be proven that the total edge irregularity strength of subdivision of star S m for m≥9 and n≥3 and the total edge irregularity strength of subdivision of star Snm1, m2, ⋯ ,mn for mi≥1, mi

Research paper thumbnail of Ramsey Number on A Union of Stars Versus A Small Cycle

Jurnal Matematika, Statistika dan Komputasi, Mar 17, 2018

The Ramsey number for a graph versus a graph , denoted by , is the smallest positive integer such... more The Ramsey number for a graph versus a graph , denoted by , is the smallest positive integer such that for any graph of order , either contains as a subgraph or ̅ contains as a subgraph. In this paper, we investigate the Ramsey numbers for stars versus small cycle. We show that and for and .

Research paper thumbnail of Total H-irregularity strength of ladder graphs

Journal of physics, May 1, 2019

Specifying parameters for a model is often a problem confronted by the developer of a game or sim... more Specifying parameters for a model is often a problem confronted by the developer of a game or simulation. It is often something which comes up after the basic relationships have been defined and coded. This paper presents the results of a survey which sought to establish some of the important parameters of a physical distribution system.

Research paper thumbnail of Bilangan Stirling dan Hubungannya dengan Beberapa Konsep Matematika

Jurnal Matematika, Statistika dan Komputasi, Feb 1, 2018

Dalam tulisan ini dibahas analogi, ekuivalensi dan keterkaitan antara bilangan-bilangan Stirling ... more Dalam tulisan ini dibahas analogi, ekuivalensi dan keterkaitan antara bilangan-bilangan Stirling dengan konsep matematika yang lain: himpunan, permutasi, fungsi, faktorial (turun dan naik), determinan-1 dan deret Maclaurin. Pada khususnya analogi antara diferensi dan turunan bisa diturunkan dengan menggunakan bilangan-bilangan Stirling. Juga ekuivalensi beberapa definisi bilangan Stirling berdasarkan konsep partisi pada permutasi dan pada himpunan serta interpretasinya, juga disajikan. Pada penerapan konsep determinan-1, diberikan dua relasi rekurensi yang berbeda tetapi ekuivalen. Relasi rekurensi yang pertama menghasilkan sebuah barisan eigen sedangkan relasi rekurensi yang kedua menghasilkan barisan eigen yang sama, tetapi diturunkan dengan menerapkan determinan-1. Kata Kunci : bilangan Stirling jenis pertama dan kedua, faktorial turun, partisi, relasi rekurensi, determinan-1.

Research paper thumbnail of Analisis Penyelesaian Persamaan Kuadrat Matriks

Jurnal Matematika, Statistika dan Komputasi, Feb 4, 2018

Persamaan kuadrat matriks dalam matriks n x n muncul dalam dunia aplikasi dan merupakan salah sat... more Persamaan kuadrat matriks dalam matriks n x n muncul dalam dunia aplikasi dan merupakan salah satu persamaan matriks nonlinier yang paling sederhana. Kita memberikan karakterisasi lengkap dari penyelesaian dalam bentuk generalisasi dekomposisi Schur. Beberapa variasi dari teknik penyelesaian numerik juga disajikan.

Research paper thumbnail of Modular Irregular Labeling On Complete Graphs

Daya Matematis: Jurnal Inovasi Pendidikan Matematika

Let G be a simple graph of n order. An edge labeling such that the weights of all vertex are diff... more Let G be a simple graph of n order. An edge labeling such that the weights of all vertex are different and elements of the set modulo n, are called a modular irregular labeling. The modular irregularity strength of G is a minimum positive integer k such that G have a modular irregular labeling. If the modular irregularity strength is none, then we called the modular irregularity strength of G is infinity. In this article, we determine the modular irregularity strength of complete graphs.

Research paper thumbnail of Pelabelan Total Tidak Teratur Titik Graf Unidentified Flying Object

Jurnal Kajian Matematika dan Aplikasinya (JKMA), Jul 31, 2022

For a graph G that have vertex set and edge set. A labelling : ∪ → {1,2,3, … , } is called a vert... more For a graph G that have vertex set and edge set. A labelling : ∪ → {1,2,3, … , } is called a vertex irregularity total k-labeling of if for any two different vertices and in have () ≠ () where () = () + ∑ () ∈ (). The smallest positive integer such that has a vertex irregular total k-labeling is called the total vertex irregularity strength of , denoted by (). In this paper, we determined the total vertex irregularity strength of Unidentified Flying Object Graph, (,). The result in this paper as follows:

Research paper thumbnail of Analisis Penyelesaian Persamaan Kuadrat Matriks

Jurnal Matematika, Statistika dan Komputasi, Feb 4, 2018

Persamaan kuadrat matriks dalam matriks n x n muncul dalam dunia aplikasi dan merupakan salah sat... more Persamaan kuadrat matriks dalam matriks n x n muncul dalam dunia aplikasi dan merupakan salah satu persamaan matriks nonlinier yang paling sederhana. Kita memberikan karakterisasi lengkap dari penyelesaian dalam bentuk generalisasi dekomposisi Schur. Beberapa variasi dari teknik penyelesaian numerik juga disajikan.

Research paper thumbnail of Bilangan Stirling dan Hubungannya dengan Beberapa Konsep Matematika

Dalam tulisan ini dibahas analogi, ekuivalensi dan keterkaitan antara bilangan-bilangan Stirling ... more Dalam tulisan ini dibahas analogi, ekuivalensi dan keterkaitan antara bilangan-bilangan Stirling dengan konsep matematika yang lain: himpunan, permutasi, fungsi, faktorial (turun dan naik), determinan-1 dan deret Maclaurin. Pada khususnya analogi antara diferensi dan turunan bisa diturunkan dengan menggunakan bilangan-bilangan Stirling. Juga ekuivalensi beberapa definisi bilangan Stirling berdasarkan konsep partisi pada permutasi dan pada himpunan serta interpretasinya, juga disajikan. Pada penerapan konsep determinan-1, diberikan dua relasi rekurensi yang berbeda tetapi ekuivalen. Relasi rekurensi yang pertama menghasilkan sebuah barisan eigen sedangkan relasi rekurensi yang kedua menghasilkan barisan eigen yang sama, tetapi diturunkan dengan menerapkan determinan-1.

Research paper thumbnail of On irregularity strength of diamond network

AKCE International Journal of Graphs and Combinatorics, 2018

In this paper we investigate the total edge irregularity strength tes(G) and the total vertex irr... more In this paper we investigate the total edge irregularity strength tes(G) and the total vertex irregularity strength tvs(G) of diamond graphs Br n and prove that tes(Br n) = ⌈(5n − 3)/3⌉, while tvs(Br n) = ⌈(n + 1)/3⌉.

Research paper thumbnail of Total H-irregularity strength of ladder graphs

Journal of Physics: Conference Series, 2019

H-irregular total labeling and total H-irregularity strength of graphs were not complete.This res... more H-irregular total labeling and total H-irregularity strength of graphs were not complete.This research aimed to determine the total H-Irregularity strength of ladder graph Lb with subgraphs C 8 and C 10.To determine of the total H-irregularity strength of ladder graphs, we have to determine the greatest lower bound and the smallest upper bound. The lower bound was analysed based on graph characteristics and other supporting theorems, while the upper bound was analysed by construct a function H-Irregular total labeling. The results reveal that the total H-Irregularity strength of ladder graph Ln with subgraph C 8 is ⌈ n − 2 i + 14 16 ⌉ ≤ t h s ( L n , C 8 ) ≤ ⌈ n + 14 18 ⌉ , for 18 i − 15 ≤ n ≤ 18 i + 2 , where i = 1,2, …, N and the total H-Irregularity strength of ladder graph Ln with subgraph C 10 is t h s ( G , H ) ≥ max { ⌈ 1 + m 1 − 1 | V ( H / S 1 ) | + | E ( H / S 1 ) | ⌉ , … , ⌈ 1 + m 1 − 1 | V ( H / S z ) | + | E ( H / S z ) | ⌉ } ⌈ n − 3 i + 18 20 ⌉ ≤ t h s ( L n , C 10 ) ≤...

Research paper thumbnail of Total edge irregularity strength of subdivision of star

Journal of Discrete Mathematical Sciences and Cryptography, 2015

Research paper thumbnail of Ramsey Number on A Union of Stars Versus A Small Cycle

The Ramsey number for a graph versus a graph , denoted by , is the smallest positive integer such... more The Ramsey number for a graph versus a graph , denoted by , is the smallest positive integer such that for any graph of order , either contains as a subgraph or ̅ contains as a subgraph. In this paper, we investigate the Ramsey numbers for stars versus small cycle. We show that and for and .

Research paper thumbnail of Pelabelan Total Tidak Teratur Titik Graf Unidentified Flying Object

Jurnal Kajian Matematika dan Aplikasinya (JKMA), Jul 31, 2022

For a graph G that have vertex set V and edge set E. A labelling f:VUE->{1,2,3,...,k} is called a... more For a graph G that have vertex set V and edge set E. A labelling f:VUE->{1,2,3,...,k} is called a vertex irregularity total k-labeling of G if for any two different vertices x and y in V have wt(x)\neq wt(y) where wt(x)=f(x)+∑_{yV(G)} f(xy). The smallest positive integer k such that G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G , denoted by tvs(G).

In this paper, we determined the total vertex irregularity strength of Unidentified Flying Object Graph, tvs(U_(m,n}). The result in this paper as follows:

tvs(U_{m,n})=(3n+1)/2 for 3<=m<=3((n+1)/2), n>=3, and

tvs(U_{m,n})=(3n+m)/3 for m>3((n+1)/2), n>=3.