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All Journal Kubik Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) Jurnal Matematika: MANTIK Jurnal Tadris Matematika KUBIK: Jurnal Publikasi Ilmiah Matematika Jurnal Riset Mahasiswa Matematika Jurnal Tadris Matematika Journal of Research on Community Engagement
Mohammad Nafie Jauhari
Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia
Arts Humanities Computer Science & IT Economics, Econometrics & Finance Education Mathematics Social Sciences

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Journal : Jurnal Matematika: MANTIK

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On the Relation of the Total Graph of a Ring and a Product of Graphs Mohammad Nafie Jauhari
Jurnal Matematika MANTIK Vol. 8 No. 2 (2022): September - November
Publisher : Mathematics Department, Faculty of Science and Technology, UIN Sunan Ampel Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15642/mantik.2022.8.2.99-104

Abstract

The total graph of a ring R, denoted as T(Γ(R)), is defined to be a graph with vertex set V(T(Γ(R)))=R and two distinct vertices u,v∈V(T(Γ(R))) are adjacent if and only if u+v∈Z(R), where Z(R) is the zero divisor of R. The Cartesian product of two graphs G and H is a graph with the vertex set V(G×H)=V(G)×V(H) and two distinct vertices (u_1,v_1 ) and (u_2,v_2 ) are adjacent if and only if: 1) u_1=u_2 and v_1 v_2∈H; or 2) v_1=v_2 and u_1 u_2∈E(G). An isomorphism of graphs G dan H is a bijection ϕ:V(G)→V(H) such that u,v∈V(G) are adjacent if and only if f(u),f(v)∈V(H) are adjacent. This paper proved that T(Γ(Z_2p )) and P_2×K_p are isomorphic for every odd prime p.
Co-Authors Ach. Nashichuddin Anisatur Rizqiyah Annisa Hardiningsih HR Anwar, Nurul Hafidhoh Armeyntan, Tata Sutrafia Bella Nafa Savitri Dayanti, Vivi Dewi Ismiarti Elly Susanti Erna Herawati, Erna Evawati Alisah Fika Wahyuni Hairur Rahman Hairur Rahman Harini, Sri Hisyam Fahmi Hisyam Fahmi Iftitahur Rohmah Ismiarti, Dewi Jannah, Shahnaz Latifatul Juhari Juhari, Juhari Lestari, Qhonita Guruh Dwi Lubab, Ahmad Mohammad Jamhuri Mufinnun, Nur Fatin Muhammad Khudzaifah Muhammad Khudzaifah Muhammad Khudzaifah Muhammad Khudzaifah Nasichuddin, Achmad Nisful Laila Novianti, Chofifah Alfin Nur Fatin Mufinnun Nurul Hafidhoh Anwar Reta, Tre Hayu Ria Risma Amelia, Risma Riyan Fahmi Syihabuddin Rizqiyah, Anisatur Safitri, Sukmawati Indah Salsabila, Wardatun Naura Salsabillah, Natasya Thalia Savitri, Bella Nafa Sri Harini Susanti, Elly Syihabuddin, Riyan Fahmi Tre Hayu Ria Reta Turmudi Turmudi, Turmudi Ulfa, Anis Maria Wahyuni, Fika Wike, Wike Nur Yulianti, Silviyatus