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All Journal InPrime: Indonesian Journal Of Pure And Applied Mathematics Journal of Mathematics Education and Science
Yulianti, Amanah
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Computer Science & IT Education Mathematics

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The Locating Chromatic Number for Amalgamation of Some Complete Graphs Yulianti, Amanah; Asmiati, Asmiati; Hamzah, Nur; Notiragayu, Notiragayu
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 6, No 1 (2024)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v6i1.38711

Abstract

The locating chromatic number of a graph is a combination of partition dimension and vertex coloring, where every two adjacent vertices are in different color classes, and all vertices have a unique color code. The amalgamation of a ≥ 2 complete graphs (K_n, n≥ 3) denoted by aK_n is obtained by identifying one vertex from each complete graph. In this paper, we present a novel study, a topic that has not been extensively explored in previous research, on locating chromatic numbers for the amalgamation of complete graphs aK_n for 2 ≤ a ≤ 6 and n≥ 3.Keywords: locating chromatic number, partition dimension, vertex coloring, color code, amalgamation of  complete graph. AbstrakBilangan kromatik lokasi graf merupakan penggabungan dari  dimensi partisi  dan pewarnaan titik, yang mana setiap dua titik bertetangga berada dalam kelas warna yang berbeda dan semua titik mempunyai kode warna yang unik. Amalgamasi dari a ≥ 2 buah graf lengkap (K_n, n≥ 3) dinotasikan dengan aK_n  diperoleh dengan cara menyatukan satu titik dari setiap graf lengkap . Pada paper ini didiskusikan hasil yang belum ada sebelumnya, yaitu bilangan kromatik lokasi amalgamasi graf lengkap aK_n untuk 2 ≤ a ≤ 6 dan n≥ 3 .Kata Kunci: bilangan kromatik lokasi, dimensi partisi, pewarnaan titik, kode warna, amalgamasi graf lengkap. 2020MSC: 05C12, 05C15
Finding The Shortest Route Between East Oku's Islamic Boarding Schools Using The Dijkstra Algorithm Amanah Yulianti; Denix Aricho Sundawa; Beni Hermansyah
Journal of Mathematics Education and Science Vol. 8 No. 2 (2025): Journal of Mathematics Education and Science
Publisher : Universitas Nahdlatul Ulama Sunan Giri Bojonegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32665/james.v8i2.5265

Abstract

This study aims to measure the distance between Islamic boarding schools in East Oku, using the Dijkstra Algorithm method to make it easier to determine the shortest route from the point of the Nurul Huda Sukaraja Islamic Boarding School to the Subulussalam Sriwangi Islamic Boarding School. In previous research, namely determining the shortest route when distributing from vegetable gardens to warehouses between toll and non-toll routes to minimize costs. In graph theory, the Dijkstra algorithm efficiently calculates the shortest path between any pair of nodes in a weighted graph, both positive and negative. This algorithm works with the principle of dynamic programming and can overcome graphs with a negative weight as long as there are no negative cycles. In its implementation, the Dijkstra algorithm iteratively updates the shortest distance between nodes by directly comparing paths with paths passing through other nodes. The advantage of this algorithm lies in its simplicity and ability to calculate the shortest distance between all pairs of nodes in a single process. The study results show that the Dijkstra Algorithm can show the fastest and most efficient alternative routes compared to conventional routes. Calculations using the Dijkstra Algorithm method produce the shortest trajectory starting from point 1-4-5 with a distance of 48 km, the most optimal route between the location and destination points.
The Locating Chromatic Number for Amalgamation of Some Complete Graphs Yulianti, Amanah; Asmiati, Asmiati; Hamzah, Nur; Notiragayu, Notiragayu
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 6 No. 1 (2024)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v6i1.38711

Abstract

The locating chromatic number of a graph is a combination of partition dimension and vertex coloring, where every two adjacent vertices are in different color classes, and all vertices have a unique color code. The amalgamation of a ≥ 2 complete graphs (K_n, n≥ 3) denoted by aK_n is obtained by identifying one vertex from each complete graph. In this paper, we present a novel study, a topic that has not been extensively explored in previous research, on locating chromatic numbers for the amalgamation of complete graphs aK_n for 2 ≤ a ≤ 6 and n≥ 3.Keywords: locating chromatic number, partition dimension, vertex coloring, color code, amalgamation of  complete graph. AbstrakBilangan kromatik lokasi graf merupakan penggabungan dari  dimensi partisi  dan pewarnaan titik, yang mana setiap dua titik bertetangga berada dalam kelas warna yang berbeda dan semua titik mempunyai kode warna yang unik. Amalgamasi dari a ≥ 2 buah graf lengkap (K_n, n≥ 3) dinotasikan dengan aK_n  diperoleh dengan cara menyatukan satu titik dari setiap graf lengkap . Pada paper ini didiskusikan hasil yang belum ada sebelumnya, yaitu bilangan kromatik lokasi amalgamasi graf lengkap aK_n untuk 2 ≤ a ≤ 6 dan n≥ 3 .Kata Kunci: bilangan kromatik lokasi, dimensi partisi, pewarnaan titik, kode warna, amalgamasi graf lengkap. 2020MSC: 05C12, 05C15
Co-Authors Asmiati Asmiati Beni Hermansyah Denix Aricho Sundawa Notiragayu, Notiragayu Nur Hamzah Nur Hamzah