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All Journal Contemporary Mathematics and Applications (ConMathA)
Rica Amalia
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Materials Science & Nanotechnology Mathematics

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Implementation of K-Means and Single Linkage on Types of Disabilities in East Java Province Putri Amaningsih; Tony Yulianto; Faisol; Rica Amalia
Contemporary Mathematics and Applications (ConMathA) Vol. 6 No. 2 (2024)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v6i2.58513

Abstract

The high number of people with disabilities is one of the problems faced by the Indonesian government, especially in Java Province. After West Java Province, East Java Province is in second place as the province with the highest rate of people with disabilities in Indonesia. Disabled people are people with physical disabilities such as not being able to walk, not being able to talk, not being able to see, and so on. The aim of this research is to group districts in East Java Province based on types of disabilities with the hope of facilitating activities in fulfilling the rights of people with disabilities in East Java Province. The grouping was carried out in order to determine the characteristics of each cluster using so that the optimal k-means method was used for clustering using the Euclidean distance method with cluster 1 in 29 districts and cluster 2 in 9 districts. The most optimal single linkage uses the Euclidean distance method with cluster 1 having 8 districts and cluster 2 having 30 districts. From the results of the validity index values, it was found that the single linkage method had the smallest validity value of the icdrate method compared to the k-means method.
Super Edge-Magic Total Labelings of ?? × ?? With ?? Pendants Rica Amalia; Kholifatur Rohmah; Khairil Anam
Contemporary Mathematics and Applications (ConMathA) Vol. 8 No. 1 (2026)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v8i1.85975

Abstract

A graph ? is defined as a finite nonempty set ? of objects called vertices (vertex for singular) together with a possibly empty set of ? ⊆ {{?, ?} ∣ ?, ? ∈ ?} called edges. One of interesting topic in graph theory is graph labelling. Super edge magic total labeling is a special form of total edge magic labeling, where vertex labels must come from the set {1,2,…,|?|}, while edge labels come from the remainder of the set {1,2,…,|?|+|?|}. Formally, this labeling is a bijective mapping: ? : ? ∪ ?→{1,2,…,|?|+|?|} with the following conditions: ?(?) ∈ {1,2,...,|?|} ∀? ∈ ? where there is a constant number ? such that for every edge ? = ?? ∈ ?, ?(?) + ?(?) + ?(?) = ?. The main focus of this research is to determine the existence and construction of super edge-magic total labeling on cartesian product graph ?? × ?? with additional pendants. In this study, we get that ?? × ?? with pendants are graphs with super edge-magic total labelling’s by constructing the labeling of their vertices and edges, thereby obtaining a magic constant ?.
Co-Authors Faisol Khairil Anam Kholifatur Rohmah Putri Amaningsih Tony Yulianto