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All Journal Journal of the Indonesian Mathematical Society Contemporary Mathematics and Applications (ConMathA) JAS (Journal of Animal Science)
Siti Zahidah
Universitas Airlangga
Agriculture, Biological Sciences & Forestry Immunology & microbiology Materials Science & Nanotechnology Mathematics Veterinary

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Connectivity Indices of Coprime Graph of Generalized Quarternion Group Zahidah, Siti; Mahanani, Dwi Mifta; Oktaviana, Karine Lutfiah
Journal of the Indonesian Mathematical Society VOLUME 27 NUMBER 3 (November 2021)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.27.3.1043.285-296

Abstract

Generalized quarternion group (Q_(4n)) is a group of order $4n$ that is generated by two elements x and y with the properties x^{2n}=y^4=e and xy=yx^{-1}. The coprime graph of Q_{4n}, denoted by Omega_{Q_{4n}}, is a graph with the vertices are elements of Q_{4n} and the edges are generated by two elements that have coprime order. The first result of this paper presented that Omega_{Q_{4n}} is a tripartite graph for n is odd and Omega_{Q_{4n}} is a star graph for n is even. The second one presented the connectivity indices of Omega_{Q_{4n}}. Connectivity indices of a graph is a research area in mathematics that popularly applied in chemistry. There are six indices that are presented in this paper, those are first Zagreb index, second Zagreb index, Wiener index, hyper-Wiener index, Harary index, and Szeged index.Generalized quaternion group (Q4n) is a group of order 4n that is generated by two elements x and y with the properties x 2n = y 4 = e and xy = yx−1 . The coprime graph of Q4n, denoted by ΩQ4n , is a graph with the vertices are elements of Q4n and the edges are formed by two elements that have coprime order. The first result of this paper presents that ΩQ4n is a tripartite graph for n is an odd prime and ΩQ4n is a star graph for n is a power of 2. The second one presents the connectivity indices of ΩQ4n . Connectivity indices of a graph is a research area in mathematics that popularly applied in chemistry. There are six indices that are presented in this paper, those are first Zagreb index, second Zagreb index, Wiener index, hyper-Wiener index, Harary index, and Szeged index.
Connectivity Indices of Coprime Graph of Generalized Quarternion Group Siti Zahidah; Dwi Mifta Mahanani; Karine Lutfiah Oktaviana
Journal of the Indonesian Mathematical Society VOLUME 27 NUMBER 3 (November 2021)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.27.3.1043.285-296

Abstract

Generalized quarternion group (Q_(4n)) is a group of order $4n$ that is generated by two elements x and y with the properties x^{2n}=y^4=e and xy=yx^{-1}. The coprime graph of Q_{4n}, denoted by Omega_{Q_{4n}}, is a graph with the vertices are elements of Q_{4n} and the edges are generated by two elements that have coprime order. The first result of this paper presented that Omega_{Q_{4n}} is a tripartite graph for n is odd and Omega_{Q_{4n}} is a star graph for n is even. The second one presented the connectivity indices of Omega_{Q_{4n}}. Connectivity indices of a graph is a research area in mathematics that popularly applied in chemistry. There are six indices that are presented in this paper, those are first Zagreb index, second Zagreb index, Wiener index, hyper-Wiener index, Harary index, and Szeged index.Generalized quaternion group (Q4n) is a group of order 4n that is generated by two elements x and y with the properties x 2n = y 4 = e and xy = yx−1 . The coprime graph of Q4n, denoted by ΩQ4n , is a graph with the vertices are elements of Q4n and the edges are formed by two elements that have coprime order. The first result of this paper presents that ΩQ4n is a tripartite graph for n is an odd prime and ΩQ4n is a star graph for n is a power of 2. The second one presents the connectivity indices of ΩQ4n . Connectivity indices of a graph is a research area in mathematics that popularly applied in chemistry. There are six indices that are presented in this paper, those are first Zagreb index, second Zagreb index, Wiener index, hyper-Wiener index, Harary index, and Szeged index.
Tentang Rumus Induksi Matematika M. Yusuf Syaifuddin; Siti Zahidah, S.Si, M.Si; Eridani
Contemporary Mathematics and Applications (ConMathA) Vol. 5 No. 1 (2023)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v5i1.43176

Abstract

This paper presents various forms of induction formulas and at the same time proves the equivalence of these formulas by proving that some of these formulas are equivalent to the Well-Ordering Principle which applies to natural number set.
Study on Sheep Animal Welfare in Traditional Farmer, Located in Agro Edutourism Mulyaharja Bogor Regency Astini, Wining; Endah Anggraeni, Henny; Barunawati Siagian, Tetty; Sulistiawati, Erni; Vibowo, Heryudianto; Wijaya Kusuma, Surya; Budiono, Dwi; Fardesiana Putri, Miranti; Zahidah, Siti; Haikal, Muhammad; Faisal, Agus
JAS Vol. 10 No. 2 (2025): Journal of Animal Science (JAS) - April 2025
Publisher : Program Studi Peternakan, Fakultas Pertanian, Sains dan Kesehatan, Universitas Timor

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32938/ja.v10i2.8441

Abstract

Indonesian farmers do not understand about the meaning of animal welfare. It makes to be difficult to implement the animal welfare. It also impacts to the production and reproduction of the animal. On the other side, the sheep livestock in Mulyaharja are maintained traditionally. This study aims to evaluate the implementation of animal welfare principle in traditional sheep farming  in Mulyaharja subdistrict. This study used purposively sampling. The data analysis method is descriptive by processing data from interviews. The Animal Needs Index were used in this study. This study highlights significant shortcomings in sheep welfare under traditional farming practices in Mulyaharja Subdistrict with average ANI index 16.49. Targeted interventions in comfort of the lie down, number days of outside/year, pasture months/year, comfort of flooring, cleanliness sheep and pen, slipperiness, ease of passage, quality of light, quality of air and air flow, ind exposure in the lying area, condition of integument and animal health.
Representation Matrices of Coprime Graph of Generalized Quaternion Group Zahidah, Siti; Zulfikar, Ahmad Nadimas; Estuningsih, Nenik; Erfanian, Ahmad
Journal of the Indonesian Mathematical Society Vol. 31 No. 3 (2025): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i3.1772

Abstract

This study discusses the representation matrices of coprime graph of generalized quaternion group. The representation matrices are adjacency matrix, antiadjacency matrix, Laplacian matrix, and signless Laplacian matrix. Furthermore, the eigenvalues of each representation matrices are determined. As the results, we obtained the construction of the four representation matrices and their eigenvalues. Based on the matrix form, we got the matrix determinant is zero, so that the matrices have zero eigenvalues except signless Laplacian matrix. As for the non-zero eigenvalues, the values depends on the type of representation matrices and the order of the graph as well as its algebraic multiplicity.
Co-Authors Anggraeni, Henny Endah astini, wining Dwi Budiono Dwi Mifta Mahanani Dwi Mifta Mahanani, Dwi Mifta Erfanian, Ahmad Eridani Erni Sulistiawati Faisal, Agus Fardesiana Putri, Miranti Heryudianto Vibowo Karine Lutfiah Oktaviana M. Yusuf Syaifuddin Muhammad Haikal Nenik Estuningsih, Nenik Oktaviana, Karine Lutfiah Siagian, Tetty Barunawati Wijaya Kusuma, Surya Zulfikar, Ahmad Nadimas