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All Journal Science and Technology Indonesia EIGEN MATHEMATICS JOURNAL
Utami, Rintang
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Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Environmental Science Materials Science & Nanotechnology Mathematics Physics

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SIFAT-SIFAT ALJABAR AMALGAMASI SEPANJANG IDEAL DAN APLIKASINYA Utami, Rintang; Wahyuni, Sri
Eigen Mathematics Journal Vol 8 No 1 (2025): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i1.261

Abstract

If given rings A and B, a ring homomorphism f : A --> B, and an ideal J of B, then a new ring can be constructed called amalgamated algebras along an ideal which is denoted by $A \bowtie^f J := {(a, f(a)+j) \mid a \in A, j \in J}$ with component-wise addition and multiplication. This paper discusses the construction, definition, properties such as isomporhisms, and characterization of amalgamated algebras along an ideal that is a prime ring and a Noetherian ring with detailed explanations. We also discuss its characterization as a reduced ring, which is a continuation from the previous paper. Furthermore, we investigate its characterization as an Artinian ring by adding an additional condition that every ideal of J has unity.
Some Properties of Generalized Token Graphs Muna, Naelufa Syifna Wifaqotul; Raventino; Utami, Rintang; Lia, Febby Desy; Huda, Muhammad Nurul; Susanti, Yeni
Science and Technology Indonesia Vol. 11 No. 2 (2026): April
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2026.11.2.643-651

Abstract

The generalized k-token graph GFk(G) is a graph with the k-subsets of V(G) as the vertices, and two different vertices are adjacent if and only if the symmetric difference contains at least one edge of G. This model extends the classical k-token graph by relaxing the adjacency condition, leading to increased edge density and altered topological properties. In this paper, we establish the fundamental properties of GFk(G), including its connectivity, duality, and monotonicity. We provide exact formulas for the vertex degrees and the total size of GF2(G), along with combinatorial bounds for k > 2. Furthermore, we characterize the girth and clique numbers, proving that GFk(G) is highly prone to containing triangles even when the base graph is triangle-free. We also explore the inheritance of Hamiltonicity and bipartiteness, demonstrating that while connectivity is preserved, bipartiteness is lost for almost all bipartite graphs with at least four vertices. Our results provide a comprehensive structural characterization of this generalization, bridging the gap between classical token graphs and broader set-theoretic graph constructions.
Co-Authors Lia, Febby Desy Muhammad Nurul Huda Muna, Naelufa Syifna Wifaqotul Raventino Sri Wahyuni Yeni Susanti