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Original Articles

Unit Graphs Associated with Rings

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Pages 2851-2871 | Received 28 Jul 2008, Published online: 18 Aug 2010

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Read on this site (10)

Barkha Baloda, Praveen Mathil & Jitender Kumar. (2024) A study of upper ideal relation graphs of rings. AKCE International Journal of Graphs and Combinatorics 21:1, pages 29-40.
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T. Ashitha, T. Asir & M. R. Pournaki. (2022) A large class of graphs with a small subclass of Cohen–Macaulay members. Communications in Algebra 50:12, pages 5080-5095.
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T. Asir, V. Rabikka, A. M. Anto & N. Shunmugapriya. (2022) Wiener index of graphs over rings: a survey. AKCE International Journal of Graphs and Combinatorics 19:3, pages 316-324.
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Meysam Rezagholibeigi, Ghodratollah Aalipour & Ali Reza Naghipour. (2022) On the spectrum of the closed unit graphs. Linear and Multilinear Algebra 70:10, pages 1871-1885.
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N. Annamalai & C. Durairajan. (2021) Linear codes from incidence matrices of unit graphs. Journal of Information and Optimization Sciences 42:8, pages 1943-1950.
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Aamir Mukhtar, Rashid Murtaza, Shafiq U. Rehman, Saima Usman & Abdul Qudair Baig. (2020) Computing the size of zero divisor graphs. Journal of Information and Optimization Sciences 41:4, pages 855-864.
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S. Kavitha & R. Kala. (2020) A note on comaximal ideal graph of commutative rings. AKCE International Journal of Graphs and Combinatorics 17:1, pages 453-460.
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T. Tamizh Chelvam & T. Asir. (2018) Genus of total graphs from rings: A survey. AKCE International Journal of Graphs and Combinatorics 15:1, pages 97-104.
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T. Tamizh Chelvam & T. Asir. (2016) Distances in zero-divisor and total graphs from commutative rings–A survey. AKCE International Journal of Graphs and Combinatorics 13:3, pages 290-298.
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T. Asir & T. Tamizh Chelvam. (2013) On the Total Graph and Its Complement of a Commutative Ring. Communications in Algebra 41:10, pages 3820-3835.
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Shouqiang Shen, Weijun Liu & Wei Jin. (2023) Laplacian eigenvalues of the unit graph of the ring . Applied Mathematics and Computation 459, pages 128268.
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Rupali S. Jain, B. Surendranath Reddy & Wajid M. Shaikh. (2023) Construction of linear codes from the unit graph G(ℤn). Asian-European Journal of Mathematics 16:11.
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Heba Adel Abdelkarim. (2023) The Geodetic Number for the Unit Graphs Associated with Rings of Order P and P2. Symmetry 15:9, pages 1799.
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Fida Moh'd & Mamoon Ahmed. (2023) Simple-intersection graphs of rings. AIMS Mathematics 8:1, pages 1040-1054.
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Kukil Kalpa Rajkhowa & Helen K. Saikia. (2022) Pendant and isolated vertices of comaximal graphs of modules. Boletim da Sociedade Paranaense de Matemática 41, pages 1-8.
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M. H. Mudaber, N. H. Sarmin & I. Gambo. (2022) Subset Perfect Codes of Finite Commutative Rings Over Induced Subgraphs of Unit Graphs. Malaysian Journal of Mathematical Sciences 16:4, pages 783-791.
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S. Pirzada & Aaqib Altaf. (2022) Co-unit graphs associated to ring of integers modulo n . Acta Universitatis Sapientiae, Mathematica 14:2, pages 308-316.
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Yonghong Liu, Abdul Rauf, AdnanAslam, Saira Ishaq & Abudulai Issa. (2022) Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of . Journal of Function Spaces 2022, pages 1-11.
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Rodney Y. Sharp. (2022) Peter Vámos, 1940–2020. Bulletin of the London Mathematical Society 54:3, pages 1145-1166.
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L. Boro, M. M. Singh & J. Goswami. (2022) Unit Graph of the Ring $$\boldsymbol{\mathbb{Z}_{m}\times\mathbb{Z}_{n}}$$. Lobachevskii Journal of Mathematics 43:2, pages 345-352.
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Khalid Louartiti. (2022) Zero-divisor graphs of small upper irredundance number. Boletim da Sociedade Paranaense de Matemática 40, pages 1-5.
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Hafiz Muahmmad Afzal Siddiqui, Ammar Mujahid, Muhammad Ahsan Binyamin & Muhammad Faisal Nadeem. (2021) On Certain Bounds for Edge Metric Dimension of Zero-Divisor Graphs Associated with Rings. Mathematical Problems in Engineering 2021, pages 1-7.
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Najat Muthana & Abdellah Mamouni. (2020) On defensive alliance in zero-divisor graphs. Journal of Algebra and Its Applications 20:09, pages 2150155.
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Nabeel E. Arif, Roslan Hasani & Nermen J. Khalel. (2021) Pseudo-Von Neumann Regular Graph of Commutative Ring. Journal of Physics: Conference Series 1879:3, pages 032012.
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Ricardo A. Podestá & Denis E. Videla. (2021) Integral equienergetic non-isospectral unitary Cayley graphs. Linear Algebra and its Applications 612, pages 42-74.
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Zhiqun Li & Huadong Su. (2021) The radius of unit graphs of rings. AIMS Mathematics 6:10, pages 11508-11515.
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M. Aijaz & S. Pirzada. (2019) Annihilating-ideal graphs of commutative rings. Asian-European Journal of Mathematics 13:07, pages 2050121.
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Zahra Barati. (2020) A study of the generalized outerplanar index of zero-divisor graphs. Afrika Matematika 31:7-8, pages 1081-1092.
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Huadong Su & Liying Yang. (2020) Domination number of unit graph of ℤn. Discrete Mathematics, Algorithms and Applications 12:05, pages 2050059.
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Huadong Su & Yangjiang Wei. (2020) Semipotent Rings Whose Unit Graphs Are Planar. Algebra Colloquium 27:02, pages 311-318.
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Huadong Su & Ling Zhu. (2020) Thickness of the subgroup intersection graph of a finite group. AIMS Mathematics 6:3, pages 2590-2606.
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Jaydeep Parejiya, Patat Sarman & Pravin Vadhel. (2020) Planarity of a unit graph: Part-I local case. Malaya Journal of Matematik 8:3, pages 1155-1157.
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Huadong Su & Yangjiang Wei. (2019) The Diameter of Unit Graphs of Rings. Taiwanese Journal of Mathematics 23:1.
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F. A. A. Almahdi, K. Louartiti & M. Tamekkante. (2018) The trace graph of the matrix ring over a finite commutative ring. Acta Mathematica Hungarica 156:1, pages 132-144.
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Ali Jafari Taloukolaei & Shervin Sahebi. (2018) Von Neumann regular graphs associated with rings. Discrete Mathematics, Algorithms and Applications 10:03, pages 1850029.
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Katherine Cooper & Brian Johnson. (2018) Zero divisor graphs of commutative graded rings. Involve, a Journal of Mathematics 11:2, pages 283-295.
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T. Asir & T. Tamizh Chelvam. (2017) Genus of total graphs of commutative rings: A survey. Electronic Notes in Discrete Mathematics 63, pages 59-68.
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Dhiren Kumar Basnet & Jayanta Bhattacharyya. (2017) Nil Clean Graphs of Rings. Algebra Colloquium 24:03, pages 481-492.
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David F. Anderson & Ayman Badawi. 2017. Groups, Modules, and Model Theory - Surveys and Recent Developments. Groups, Modules, and Model Theory - Surveys and Recent Developments 23 39 .
Raibatak Sen Gupta & M.K. Sen. (2016) Some new results on the graph Γ1(R) over a ring R. Electronic Notes in Discrete Mathematics 53, pages 3-14.
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Ali Reza Naghipour & Meysam Rezagholibeigi. (2016) A REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF A FINITE RING. Bulletin of the Korean Mathematical Society 53:4, pages 1197-1211.
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Krishnan Selvakumar & Manoharan Subajini. (2016) Classification of rings with toroidal Jacobson graph. Czechoslovak Mathematical Journal 66:2, pages 307-316.
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S. Akbari, E. Estaji & M.R. Khorsandi. (2015) On the Unit Graph of a Non-commutative Ring. Algebra Colloquium 22:spec01, pages 817-822.
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Mojgan Afkhami, Zahra Barati & Kazem Khashyarmanesh. (2014) When the line graphs of the unit, unitary and total graphs are planar and outerplanar. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 56:2, pages 479-490.
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Huadong Su, Kenta Noguchi & Yiqiang Zhou. (2014) Finite commutative rings with higher genus unit graphs. Journal of Algebra and Its Applications 14:01, pages 1550002.
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S. Kiani, H. R. Maimani & S. Yassemi. (2014) Well-Covered and Cohen–Macaulay Unitary Cayley Graphs. Acta Mathematica Hungarica 144:1, pages 92-98.
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Ashish Das, H. R. Maimani, Mohammad Pournaki & Siamak Yassemi. (2014) Nonplanarity of unit graphs and classification of the toroidal ones. Pacific Journal of Mathematics 268:2, pages 371-387.
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M. Afkhami, Z. Barati & K. Khashyarmanesh. (2014) When the unit, unitary and total graphs are ring graphs and outerplanar. Rocky Mountain Journal of Mathematics 44:3.
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Mojgan Afkhami, Zahra Barati & Kazem Khashyarmanesh. (2013) A graph associated to a lattice. Ricerche di Matematica 63:1, pages 67-78.
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T. Asir & T. Tamizh Chelvam. (2013) On the genus of generalized unit and unitary Cayley graphs of a commutative ring. Acta Mathematica Hungarica 142:2, pages 444-458.
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HUADONG SU & YIQIANG ZHOU. (2013) ON THE GIRTH OF THE UNIT GRAPH OF A RING. Journal of Algebra and Its Applications 13:02, pages 1350082.
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Ayman Badawi. 2014. Commutative Algebra. Commutative Algebra 39 54 .
Mojgan Afkhami & Fahimeh Khosh-Ahang. (2013) Unit graphs of rings of polynomials and power series. Arabian Journal of Mathematics 2:3, pages 233-246.
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DAVID F. ANDERSON & AYMAN BADAWI. (2013) THE GENERALIZED TOTAL GRAPH OF A COMMUTATIVE RING. Journal of Algebra and Its Applications 12:05, pages 1250212.
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T. TAMIZH CHELVAM & T. ASIR. (2013) THE INTERSECTION GRAPH OF GAMMA SETS IN THE TOTAL GRAPH OF A COMMUTATIVE RING-I. Journal of Algebra and Its Applications 12:04, pages 1250198.
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F. Heydari & M. J. Nikmehr. (2012) The unit graph of a left Artinian ring. Acta Mathematica Hungarica 139:1-2, pages 134-146.
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Kazem Khashyarmanesh & Mahdi Reza Khorsandi. (2012) A generalization of the unit and unitary Cayley graphs of a commutative ring. Acta Mathematica Hungarica 137:4, pages 242-253.
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Z. BARATI, K. KHASHYARMANESH, F. MOHAMMADI & KH. NAFAR. (2012) ON THE ASSOCIATED GRAPHS TO A COMMUTATIVE RING. Journal of Algebra and Its Applications 11:02, pages 1250037.
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