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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Muhammad Husnul Khuluq
Department of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Surabaya
Mathematics

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On A-Distance (Anti)magic Labeling of Prime Graph over the Ring Zn Muhammad Husnul Khuluq
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.v11i1.41237

Abstract

Let G = (V, E) be a simple graph with n vertices, and let A be an abelian group of order n. Let f: V(G) → A be a bijection, and define the weight of a vertex x by w(x) = Σy ∈ N(x) f(y), where N(x) denotes the open neighborhood of x. We call f an A-distance magic labeling if all vertex weights are equal, and an A-distance antimagic labeling if the weights of distinct vertices are pairwise different. The prime graph of a commutative ring R is the simple graph with vertex set R in which two vertices x and y are adjacent if and only if xRy = {0}. In this paper, we investigate the existence of A-distance magic and A-distance antimagic labelings of the prime graph over the ring Zn for several values of n.
Application of a Heterogeneous Graph for Analyzing Workforce Competency Networks Nasya Lailatur Romadona; Muhammad Husnul Khuluq
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (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.v11i2.46006

Abstract

Recruitment in outsourcing companies requires effective matching between candidate competencies and job requirements. This study constructs and analyzes a heterogeneous candidatecompetencyposition graph using real recruitment data from an outsourcing company to examine the structural roles of competencies and their community organization. The recruitment database comprised 28,289 records collected from October 2025 to August 2026, with 875 unique candidates across five selected positions: Fitter, Maintenance, Mechanical Technician, Electrical Technician, and Welder. Using stratified, criterion-based purposive sampling with equal allocation, 20 candidates were selected from each position, resulting in 100 candidates. The resulting graph contained 115 vertices and 665 edges, consisting of 634 candidatecompetency relationships and 31 competencyposition relationships. Normalized betweenness centrality ranked Technical Drawing Reading highest (CB = 0.197077), followed by Welding (0.185315) and Teamwork (0.141790). Louvain community detection with resolution 1.0, weight=None, and random seed 38 identified five communities with modularity Q = 0.079237. A 30-run stability analysis produced three to six communities, with a mean pairwise ARI of 0.137730, indicating variation across random initializations. The findings are interpreted as exploratory structural patterns rather than statistically representative community structures.
Co-Authors Nasya Lailatur Romadona