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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Semeton Mathematics Journal
Purnamasari, Dara
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Mathematics

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The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group Asmarani, Evi Yuniartika; Lestari, Sahin Two; Purnamasari, Dara; Syarifudin, Abdul Gazir; Salwa, Salwa; Wardhana, I Gede Adhitya Wisnu
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v7i4.16991

Abstract

Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph. A power graph of the group G is defined as a graph whose vertex set is all elements of G and two distinct vertices a and b are adjacent if and only if  or  for a positive integer  and . In addition to mathematics, graph theory can be applied to various fields of science, one of which is chemistry, which is related to topological indices. In this study, the topological indexes will be discussed, namely the Zagreb index, the Wiener index, and the Gutman index of the power graph of the dihedral group  where  with  prime numbers and an  natural number. The method used in this research is a literature review. The results obtained from this study are the first Zagreb index, Wiener index, and Gutman index of the power graph of the dihedral group  where  where  is prime and an m natural number respectively is .
Traffic Waiting Time Optimization: An Effective Effort to Overcome Congestion at Gede Ngurah Cakranegara Intersection Setiawati, Setiawati; Rahmi, Dhea Wasila; Syauqi, Shofiyurrahman; Purnamasari, Dara
Semeton Mathematics Journal Vol 1 No 1 (2024): April
Publisher : Program Studi Matematika

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/semeton.v1i1.206

Abstract

Intersections are places that are prone to traffic congestion. This is due to the location and function of the intersection, which if left unchecked will lead to accidents. To overcome this problem, traffic lights are made to regulate traffic flow conditions. Gede Ngurah Cakranegara Intersection is an intersection that has high congestion conditions, this is due to its location in the city center and its function as a main road. In addition, the trigger for congestion at the Gede Ngurah Cakranegara intersection is the waiting time which is still not optimal and the lack of orderly drivers in obeying the traffic lights. Thus, the purpose of this study is to optimize the total waiting time at the Gede Ngurah Cakranegara intersection. Total waiting time optimization is done using compatible graph. The compatible graph in this case will describe the condition of traffic flows that will run simultaneously without interfering with each other, so that they are safe and do not collide with each other. This study uses primary data obtained from field observations conducted in the morning, afternoon and evening. After optimization, the total waiting time at the Gede Ngurah Cakranegara intersection following the light signal is 180 seconds and the total waiting time for those who do not follow the light signal is 120 seconds. Compared to the previous waiting time of 538 seconds, a more optimal time was obtained.
Co-Authors Asmarani, Evi Yuniartika I Gede Adhitya Wisnu Wardhana Lestari, Sahin Two Rahmi, Dhea Wasila Salwa Salwa Setiawati Setiawati Syauqi, Shofiyurrahman