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Syarat Regularitas dan Eulerian Graf Unit dari Ring Z_n Kurniawan, Vika Yugi; Nisa, Lailatul Chairul
KUBIK Vol 9 No 1 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v9i1.33693

Abstract

Let be a ring of integers modulo and denote the set of all unit elements of the ring. The unit graph of which is denoted by is a simple graph, where the vertices of are all elements of, where two different vertices and are connected by an edge if and only if is the unit of. In this article, we will examine the properties of the unit graph of the ring. The results of this study show that is an Euler graph if where is even, and is a regular graph if is even.
Marketing Refurbished Products with Carbon-Emission-Constraint Policy and Consumer Behavior: Offline vs. Online Channels Nughthoh Arfawi Kurdhi; Yahya Putra Pradana; Yogi Pasca Pratama; Vika Yugi Kurniawan
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 10 No. 2 (2024)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j24775401.ijcsam.v10i2.4570

Abstract

Refurbished products, which are repaired or restored to a like-new condition, offer a more sustainable alternative to new products by extending their lifecycle. However, the marketing of refurbished products faces several chal-lenges, including consumer perception, trust, and the impact of carbonemission-constraint policies. This study aims to address these challenges and provide recommendations for effective marketing strategies. We explore the marketing of refurbished products within the context of carbon-emission-constraint policies, specifically comparing offline and online channels. We present two channel models, with the first model, referred to as Model O, fo-cusing on marketing refurbished products through the manufacturer’s own e-commerce channel. The second model, known as Model T, explores the al-ternative approach of outsourcing the marketing activity to a third-party en-tity. Carbon-emissionconstraint policies impose restrictions on businesses’ carbon footprint, affecting their marketing strategies. Businesses must navi-gate these policies while effectively promoting refurbished products to envi-ronmentally conscious consumers. By addressing the challenges faced in marketing refurbished products with carbon-emission-constraint policies, consumer behavior, and comparing offline and online channels, this thesis aims to provide valuable insights for businesses and policymakers to effec-tively promote sustainable consumption and contribute to a more environ-mentally conscious industry.
Connectivity of The Triple Idempotent Graph of Ring Zn Vika Yugi Kurniawan; Bayu Purboutomo; Sutrima Sutrima; Nughthoh Arfawi Kurdhi
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 10 No. 1 (2024)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

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Abstract

The Triple Total Graph of The Ring Zn Vika Yugi Kurniawan; Syaifudin Zyuhri; Santoso Budi Wiyono
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41488

Abstract

Let R be a commutative ring and let Z(R) denotes the set of zero-divisors of R. The triple total graph of R, denoted by TT(R), is a simple graph whose vertex set is R∖{0}. Two distinct vertices v1 and v2 are adjacent in TT(R) if and only if v1+v2∉Z(R) and there exists v3∈R∖{0}, with v3≠v1 and v3≠v2, such that v1+v3∉Z(R),  v2+v3∉Z(R), and v1+v2+v3∈Z(R).In this paper, we investigate the structural properties of the graph TT(Zn). We show that if n is even with n 2, then TT(Zn) is an empty graph. When n is prime with 2 n 11, the graph TT(Zn) is disconnected. In contrast, for prime integers n≥ 11, the graph becomes connected with diam(TT(Zn))=2 and gr(TT(Zn))=3. Moreover, each vertex has degree n−5, implying that the graph is (n−5)-regular and consequently both Eulerian and Hamiltonian. These results illustrate how the arithmetic nature of n determines the global structure of the triple total graph.