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All Journal Journal of Mathematics Education and Science Prismatika: Jurnal Pendidikan dan Riset Matematika
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On Local Vertex Antimagic Total Coloring Of Path, Cycle, And Star Graphs With Comb Operation Taradita Ayitia Meisya Fendina; Desi Febriani Putri; Wasono; Maria Alensia Deltin Dala
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.v8i2.4777

Abstract

Let G(V,E) be a graph consisting of a set of vertices V(G) and a set of edges E(G) where the number of vertices and edges are denoted by |V(G)| and |E(G)|, respectively. A bijective function f:V(G) \vee E(G) \to {1,2,3,...,(|V(G)|+|E(G)|)} is defined as a local vertex antimagic total coloring if there exist two adjacent vertex vx and vy with . Therefore, every local vertex antimagic total coloring produces a vertex coloring of the graph G, where each vertex v is assigned a color corresponding to its weight w(v). This research is essential as it contributes to development of graph coloring theory, particularly in the area of local vertex antimagic total coloring, which has been rarely studied. This research discusses the local vertex antimagic total coloring of and  which aims to determine the chromatic number. The result of the research is the chromatic number of local vertex antimagic total coloring of  and the chromatic number of local vertex antimagic total coloring , is if  is odd and  if  is even.
Local Antimagic Edge Coloring Of Gear Graphs And Semi Parachute Graphs Dian Sri Rahmadani; Desi Febriani Putri; Wasono; Hardina Sandariria
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.v8i2.4775

Abstract

The graph G is a pair of sets consisting of a vertex set V(G) and an edge set E(G), denoted by G = (V (G),E(G)). Coloring a graph involves assigning colors to each vertex, edge, or region such that no adjacent vertices, edges, or regions share the same color. A bijective function f∶ V (G) → {1,2,3,...,|V (G)|} is called a local edge antimagic coloring if for any two adjacent edges e_1 and e_2, they have different weights, w(e_1) ≠ w(e_2), where e = uv ∈ E(G) and w(e) = f (u)+f (v). The chromatic number is the term used in the context of local antimagic coloring, referring to the minimum number of colors derived from local antimagic labeling. This research discusses the local antimagic edge coloring on the Gear Graph (G_n) and the Semi Parachute Graph (SP_(2n-1)). The aim of the research is to determine the chromatic number of local antimagic edge coloring χlea(G) for the researched graphs. The method used in this research is pattern detection to derive the general pattern. Based on the analysis, the chromatic number of local antimagic edge coloring is obtained for the Gear Graph (G_n) and the Semi Parachute Graph (SP_(2n-1)) are χlea (G_n)=n + 2 and χlea(SP_(2n-1) )=n+ 2.
ANALISIS TEORI PERMAINAN DENGAN RANTAI MARKOV UNTUK PENENTUAN STRATEGI OPTIMAL DAN PERPINDAHAN PENGGUNA PADA OJEK ONLINE Arma, Abdul; Wasono; Amijaya, Fidia Deny Tisna
Prismatika: Jurnal Pendidikan dan Riset Matematika Vol. 8 No. 2 (2026): Prismatika: Jurnal Pendidikan dan Riset Matematika
Publisher : Universitas Insan Budi Utomo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33503/prismatika.v8i2.3051

Abstract

The development of transportation services in Indonesia has led to increasing competition among online motorcycle taxi service providers, particularly between Gojek and Grab. This competition is not limited to pricing aspects but also includes promotional offers and vouchers, ease of application use, service completeness, payment methods, and the quality of driver services. These conditions potentially affect user loyalty and encourage customer switching behavior. This study aims to determine the optimal competitive strategies between Gojek and Grab and to analyze user switching patterns. The data used in this study are primary data obtained through questionnaires distributed to students of Mulawarman University who use online motorcycle taxi services. Game theory is applied to model competition between two players in a zero-sum game framework, where each company acts rationally in selecting strategies to maximize relative profits against its competitor. The payoff matrix is constructed based on questionnaire results and analyzed using pure strategies to determine the optimal strategy through the saddle point value. Markov chains are employed to analyze user switching behavior by modeling transition probabilities between states, namely Gojek and Grab, and to estimate the distribution of users in future periods until reaching a steady-state condition. The results indicate that the optimal strategy based on game theory, with Gojek as the row player and Grab as the column player, is the promotional and voucher strategy with a saddle point value of −10. Markov chain analysis shows that the probability of users switching from Gojek to Grab is 0,14 while the probability of switching from Grab to Gojek is 0.04. The steady-state condition is achieved in the 28th period, with user probabilities of 0,223 for Gojek and 0,777 for Grab. These findings indicate that, in the long run, students of Mulawarman University tend to switch from Gojek to Grab.
Co-Authors Arma, Abdul Desi Febriani Putri Dian Sri Rahmadani Fidia Deny Tisna Amijaya Hardina Sandariria Maria Alensia Deltin Dala Taradita Ayitia Meisya Fendina