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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi International Journal of Computing Science and Applied Mathematics-IJCSAM
Rinurwati Rinurwati
Institut Teknologi Sepuluh Nopember
Mathematics

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Bi-Edge Metric Dimension of Graphs Rinurwati Rinurwati; Fadillah Dian Maharani
(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

Given a connected G = (V(G),E(G)) graph. The main problem in graph metric dimensions is calculating the metric dimensions and their characterization. In this research, a new dimension concept is introduced, namely a bi-edge metric dimension of graph which is a development of the concpet of bi-metric graphs with the innovation of bi-metric graph representations to become the bi-edge metric graph representations. In this case, what is meant by bi-edge metric and edge detour. If there is a set in G that causes every edge in G has a different bi-edge metric representation in G, then that set is called the biedge metric resolving set. The minimum cardinality of the bi-edge metric resolving set graphs is called the bi-edge metric dimension of G graph, denoted by edimb(G). The spesific purpose of this research is to apply the concept of bi-edge metric dimensions to special graphs, such as cycle, complete, star and path can be obtained.
Approximation Properties on a Set Based on Equivalence Relations and Dominance Relations Dian Winda Setyawati; Soleha Soleha; Rinurwati Rinurwati
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): 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/cauchy.v11i1.40603

Abstract

 An equivalence relation on a set forms equivalence classes so that the concept of approximation is formed on that set (rough set). The concept of approximation on a set is developing very rapidly. Some papers replace the equivalence relation with other relations, one of which is the dominance relation. The symmetry property of the equivalence relation is replaced by the anti-symmetry property so that a dominance relation is formed. This paper reviews several papers related to approximation on a set $w.r.t$ equivalence  and dominance relations by describing the approximation properties that hold in both relations in terms of the concept of 3 types of approximation on a set. This paper also provides the approximation properties that hold in the equivalence relation but do not hold in the dominance relations in terms of the concept of 3 types of approximation on a set. The main contribution of this paper is showing that the relationship between the concept of 3 types of approximation on a set $w.r.t$ the equivalence relation and the dominance relation.
Co-Authors Dian Winda Setyawati Fadillah Dian Maharani Soleha Soleha