[1] S. Akbari, D. Kiani, F. Mohammadi, and S. Moradi, The total graph and regular graph of a commutative ring, J. Pure Appl. Algebra 213 (2009), no. 12, 2224–2228.
[2] S. Akbari, H.R. Maimani, and S. Yassemi, When a zero-divisor graph is planar or a complete r-partite graph, J. Algebra 270 (2003), no. 1, 169–180.
[3] S. Akbari and A. Mohammadian, On the zero-divisor graph of a commutative ring, J. Algebra 274 (2004), no. 2, 847–855.
[4] S. Akbari and R. Nikandish, Some results on the intersection graph of ideals of matrix algebras, Linear Multilinear Algebra 62 (2014), no. 2, 195–206.
[5] S. Akbari, R. Nikandish, and M.J. Nikmehr, Some results on the intersection graphs of ideals of rings, J. Algebra Appl. 12 (2013), no. 4, Article ID: 1250200.
[6] A. Alilou and J. Amjadi, The sum-annihilating essential ideal graph of a commutative ring, Commun. Comb. Optim. 1 (2016), no. 2, 117–135.
[7] J. Amjadi, R. Khoeilar, and A. Alilou, The annihilator-inclusion ideal graph of a commutative ring, Commun. Comb. Optim. 6 (2021), no. 2, 231–248.
[8] D. D. Anderson and M. Naseer, Beck’s coloring of a commutative ring, J. Algebra 159 (1993), no. 2, 500–514.
[9] D. F. Anderson, R. Levy, and J. Shapiro, Zero-divisor graphs, von Neumann regular rings, and Boolean algebras, J. Pure Appl. Algebra 180 (2003), no. 3, 221–241.
[10] D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), no. 2, 434–447.
[11] M.F. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Company, Reading, Mass.-London-Don Mills Ont, 1969.
[12] F.G. Ball, D.J. Sirl, and P.S. Trapman, Epidemics on random intersection graphs, Ann. Appl. Probab. 24 (2014), no. 3, 1081–1128.
[13] I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), no. 1, 208–226.
[14] M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings I, J. Algebra Appl. 10 (2011), no. 4, 727–739.
[15] M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings II, J. Algebra Appl. 10 (2011), no. 04, 741–753.
[16] P. J. Bernhard, S. T. Hedetniemi, and D. P. Jacobs, Efficient sets in graphs, Discrete Appl. Math. 44 (1993), no. 1-3, 99–108.
[17] F. Bernhart and P. C. Kainen, The book thickness of a graph, J. Combin. Theory Ser. B 27 (1979), no. 3, 320–331.
[18] J. R. S. Blair, The efficiency of AC graphs, Discrete Appl. Math. 44 (1993), no. 1-3, 119–138.
[19] M. Bloznelis, J. Jaworski, and K. Rybarczyk, Component evolution in a secure wireless sensor network, Networks 53 (2009), no. 1, 19–26.
[20] J.A. Bondy, Pancyclic graphs I, J. Combin. Theory Ser. B 11 (1971), no. 1, 80–84.
[21] L. Boro, M. M. Singh, and J. Goswami, Line graph associated to the intersection graph of ideals of rings, J. Math. Comput. Sci. 11 (2021), no. 3, 2736–2745.
[22] J. Bosak, The graphs of semigroups, Theory of Graphs and Application (M. Fielder, ed.), Academic Press, New York, 1964, pp. 119–125.
[23] M. Bradonjic, A. Hagberg, N. Hengartner, and A. Percus, Component evolution in general random intersection graphs, Workshop on Algorithms and Models for the Web Graph (WAW), 2010, pp. 36–49.
[24] W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993.
[25] N. Cairnie and K. Edwards, Some results on the achromatic number, J. Graph Theory 26 (1997), no. 3, 129–136.
[26] I. Chakrabarty, S. Ghosh, T.K. Mukherjee, and M. K. Sen, Intersection graphs of ideals of rings, Discrete Math. 309 (2009), no. 17, 5381–5392.
[27] G. Chartrand, J. Hallas, E. Salehi, and P. Zhang, Rainbow mean colorings of graphs, Discrete Math. Lett. 2 (2019), 18–25.
[28] G. Chartrand and F. Harary, Planar permutation graphs, Ann. Inst. Henri Poincare Sect., vol. 3, 1967, pp. 433–438.
[29] G. Chartrand, F. Harary, and P. Zhang, On the geodetic number of a graph, Networks 39 (2002), no. 1, 1–6.
[30] G. Chartrand, T. W. Haynes, M. A. Henning, and P. Zhang, Detour domination in graphs, Ars Combin. 71 (2004), 149–160.
[31] G. Chartrand, T. Thomas, V. Saenpholphat, and P. Zhang, A new look at Hamiltonian walks, Bull. Inst. Combin. Appl. 42 (2004), 37–52.
[32] G. Chartrand and P. Zhang, Convex sets in graphs, Congr. Numer. 136 (1999), 19–32.
[33] P. Chen, A kind of graph structure of rings, Algebra Colloquium 10 (2003), no. 2, 229–238.
[34] H.J. Chiang-Hsieh, Classification of rings with projective zero-divisor graphs, J. Algebra 319 (2008), no. 7, 2789–2802.
[35] C.A. Christen and S.M. Selkow, Some perfect coloring properties of graphs, J. Combin. Theory Ser. B 27 (1979), no. 1, 49–59.
[36] G. Cooperman and L. Finkelstein, New methods for using cayley graphs in interconnection networks, Discrete Appl. Math. 37/38 (1992), 95–118.
[37] J. T. Cross, The Euler φ− function in the Gaussian integerss, Amer. Math. Monthly 90 (1983), no. 8, 518–528.
[38] B. Csákány and G. Pollák, The graph of subgroups of a finite group, Czech. Math. J. 19 (1969), no. 2, 241–247.
[39] A. Das, On perfectness of intersection graph of ideals of Zn, Discuss. Math. Gen. Algebra Appl. 37 (2017), no. 2, 119–126.
[40] B. Deng and X. Li, More on l-borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 77 (2017), no. 1, 115–127.
[41] G. Dresden and W.M.
Dymàček, Finding factors of factor rings over the Gaussian integers, Amer. Math. Monthly 112 (2005), no. 7, 602–611.
[42] E.E. Enochs and M.G.J Overtoun, Relative homological algebra, de Gruyter Exp. Math., vol. 30, de Gruyter, Berlin, 2000.
[43] P. Erdös, A. W. Goodman, and L. Pósa, The representation of a graph by set intersections, Canad. J. Math. 18 (1966), 106–112.
[44] S. Ghosh, Counting number of factorizations of a natural number, arXiv:0811.3479, 2008.
[45] S. C. Gong, X. Li, G. H. Xu, I. Gutman, and B. Furtula, Borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 74 (2015), no. 2, 321–332.
[46] K.R. Goodearl and R.B. Warfield, An introduction to noncommutative noetherian rings, in: London Math. Soc. Student Text Series, Vol. 16, Cambridge Univ. Press, Cambridge, 1989.
[47] R.P. Grimaldi, Graphs from rings, Congr. Numer. 71 (1990), 95–103.
[48] P. M. Grundy, Mathematics and games, Eureka 2 (1939), 6–9. Reprinted in Eureka: The Archimedeans’ Journal, 27 (1964), 9–11.
[49] S.L. Hakimi, J. Mitchem, and E.F. Schmeichel, Degree-bounded coloring of graphs: variations on a theme by brooks, J. Graph Theory 20 (1995), no. 2, 177–194.
[50] F. Harary, On the notion of balance of a signed graph, Michigan Math. J. 2 (1953), no. 2, 143 – 146.
[51] F. Harary, Graph Theory, Addison-Wesley, Reading, Mass., 1969.
[52] F. Harary, The achromatic number of a graph, J. Combin. Theory 8 (1970), 154–161.
[53] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
[54] S.M. Hedetniemi, S.T. Hedetniemi, and T. Beyer, A linear algorithm for the grundy (coloring) number of a tree, Congr. Numer. 36 (1982), 351–363.
[55] W. Heinzer and J. Ohm, Locally Noetherian commutative rings, Trans. Amer. Math. Soc. 158 (1971), no. 2, 273–284.
[56] C. Hernando, T. Jiang, M. Mora, I. M. Pelayo, and C. Seara, On the steiner, geodetic and hull numbers of graphs, Discrete Math. 293 (2005), no. 1-3, 139–154.
[57] M.-C. Heydemann, Cayley graphs and interconnection networks, Graph Symmetry. NATO ASI Series (Series C: Mathematical and Physical Sciences) (G. Hahn and G. Sabidussi, eds.), vol. 497, Springer, 1997, pp. 167–224.
[58] N. Hoseini, A. Erfanian, A. Azimi, and M. Farrokhi D. G., On cycles in intersection graph of rings, Bull. Iranian Math. Soc. 42 (2016), no. 2, 461–470.
[59] D. F. Hsu, Introduction to a special issue on interconnection networks, Networks 23 (1993), no. 2, 211–213.
[60] T.W. Hungerford, Algebra, Springer, New York, USA, 8th edition, 1996.
[61] S. H. Jafari and N. J. Rad, Planarity of intersection graphs of ideals of rings, Int. Electron. J. Algebra 8 (2010), 161–166.
[62] S.H. Jafari and N. J. Rad, Domination in the intersection graphs of rings and modules, Ital. J. Pure Appl. Math. 28 (2011), no. 2, 17–20.
[63] I. Kaplansky, Commutative Rings, Revised Edition, University of Chicago Press, Chicago, 1974.
[64] S. Krishnan and P. Subbulakshmi, Classification of rings with toroidal annihilating-ideal graph, Commun. Comb. Optim. 3 (2018), no. 2, 93–119.
[65] M. Kubale, Graph Colorings, American Mathematical Society, Providence, R, 2004.
[66] K. Kuratowski, Sur le proble´me des courbes gauches en topologie, Fund. Math. 15 (1930), no. 1, 271–283.
[67] T. Y. Lam, A First Course in Non-commutative Rings, Graduate Texts in Mathematics, Vol. 131, Springer-Verlag, Berlin/Heidelberg, New York, 1991.
[68] D. S. Malik, M. K. Sen, and S. Ghosh, Introduction to Graph Theory, Cengage Learning, New York, 2014.
[69] D.S. Malik, J.M. Mordeson, M.K. Sen, and S. Ghosh, Fundamentals of Abstract Algebra, The McGraw-Hill Companies Inc., 1997.
[70] W. Massey, Algebraic Topology: An Introduction, Harcourt, Brace & World, Inc., New York, 1967.
[71] T. A. McKee and F. R. McMorris, Topics in Intersection Graph Theory, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1999.
[72] R. Nikandish and M. J. Nikmehr, The intersection graph of ideals of Zn is weakly perfect, Util. Math. 101 (2016), 329–336.
[73] E. A. Osba, The intersection graph for finite commutative principal ideal rings, Acta Math. Acad. Paedagog. Nyh´azi. (N.S.) 32 (2016), no. 1, 15–22.
[74] E. A. Osba, S. Al-Addasi, and O. Abughneim, Some properties of the intersection graph for finite commutative principal ideal rings, Int. J. Combin. 2014 (2014), Article ID: 952371.
[75] M.J. Plantholt, The chromatic index of graphs with large maximum degree, Discrete Math. 47 (1983), 91–96.
[76] Z. S. Pucanović and Z. Z. Petrović, Toroidality of intersection graphs of ideals of commutative rings, Graphs Combin. 30 (2014), no. 3, 707–716.
[77] Z. S. Pucanović, M. Radovanović, and A. L. J. Erić, On the genus of the intersection graph of ideals of a commutative ring, J. Algebra Appl. 13 (2014), no. 5, Article ID: 1350155, 20 pages.
[78] N. J. Rad, S. H. Jafari, and S. Ghosh, On the intersection graphs of ideals of direct product of rings, Discuss. Math. Gen. Algebra Appl. 34 (2014), no. 2, 191–201.
[79] P. M. Rad and P. Nasehpour, On graphs of bounded semilattices, Math. Notes 107 (2020), 264–273.
[80] V. Ramanathan, On projective intersection graph of ideals of commutative rings, J. Algebra Appl. 20 (2021), no. 2, Article ID: 2150017.
[81] S.P. Redmond, An ideal-based zero-divisor graph of a commutative ring, Comm. Algebra 31 (2003), no. 9, 4425–4443.
[82] G. Ringel and J.W.T. Youngs, Solution of the Heawood map-coloring problem, Proc. Natl. Acad. Sci. USA 60 (1968), 438–445.
[83] S. Sajana, D. Bharathi, and K.K. Srimitra, Signed intersection graph of ideals of a ring, Int. J. Pure Appl. Math. 113 (2017), no. 10, 175–183.
[84] K. Selvakumar and P. Subbulakshmi, On the crosscap of the annihilating-ideal graph of a commutative ring, Palestine J. Math. 7 (2018), no. 1, 151–160.
[85] P. Sharma, A. Gaur, and M. Acharya, C −consistency in signed total graphs of commutative rings, Discrete Math. Algorithms Appl. 8 (2016), no. 3, Article ID: 1650041.
[86] A. Simis, W. V. Vasconcelos, and R. H. Villarreal, On the ideal theory of graphs, J. Algebra 167 (1994), no. 2, 389–416.
[87] S. Spiroff and C. Wickham, A zero divisor graph determined by equivalence classes of zero divisors, Comm. Algebra 39 (2011), no. 7, 2338–2348.
[88] E. Szpilrajn-Marczewski, Sur deux proprie/‘ete/‘s des classes dénsembles (in french), Fund. Math. 33 (1945), no. 1, 303–307.
[89] E. Szpilrajn-Marczewski, Sur deux propriétés des classes dénsembles, Fund. Math. 33 (1945), no. 1, 303–307, (Trans. Bronwyn Burlingham. ”A Translation of Sur deux propriétés des classes dénsembles,” University of Alberta, 2009).
[90] A. A. Talebi, A kind of intersection graphs on ideals of a ring, J. Math. Stat. 8 (2012), no. 1, 82–84.
[91] T. Tamizh Chelvam and T. Asir, The intersection graph of gamma sets in the total graph of a commutative ring I, J. Algebra Appl. 12 (2013), no. 4, Article ID: 1250198.
[92] , On the genus of the total graph of a commutative ring, Comm. Algebra 41 (2013), no. 1, 142–153.
[93] C. Thomassen, The graph genus problem is NP-complete, J. Algorithms 10 (1989), no. 4, 568–576.
[94] P. Vadhel, Some results on intersection graphs of ideals of commutative rings, Int. J. Math. Appl. 8 (2020), no. 1, 69–75.
[95] P. Vadhel and S. Visweswaran, Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case, Algebra Discrete Math. 26 (2018), no. 1, 130–143.
[96] , Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, quasilocal case, Algebra Discrete Math. 27 (2019), no. 1, 117–143.
[97] S. Visweswaran and J. Parejiya, Some results on a supergraph of the comaximal ideal graph of a commutative ring, Commun. Comb. Optim. 3 (2018), no. 2, 151–172.
[98] S. Visweswaran and P. Vadhel, Some results on a spanning subgraph of the intersection graph of ideals of a commutative ring, Math. Today 31 (2015), 1–20.
[99] , Some results on a subgraph of the intersection graph of ideals of a commutative ring, J. Algebra Relat. Topics 6 (2018), no. 2, 35–61.
[100] H. Wang, Zero-divisor graphs of genus ones, J. Algebra 304 (2006), no. 2, 666–678.
[101] D. B. West, Introduction to Graph Theory, Prentice Hall, Upper Saddle River, NJ, 2001.
[102] A. T. White, Graphs, Groups and Surfaces, Amsterdam, North-Holland Pub. Co.; New York, American Elsevier Pub. Co., 1973.
[103] C. Wickham, Classification of rings with genus one zero-divisor graphs, Comm. Algebra 36 (2008), no. 2, 325–345.
[104] , Rings whose zero-divisor graphs have positive genus, J. Algebra 321 (2009), no. 2, 377–383.
[105] J.-M. Xu, On bondage numbers of graphs: A survey with some comments, Int. J. Combin. 2013 (2013), Article ID: 595210.
[106] M. Zaker, Inequalities for the grundy chromatic number of graphs, Discrete Appl. Math. 155 (2007), no. 18, 2567–2572.
[107] T. Zaslavsky, A mathematical bibliography of signed and gain graphs and allied areas, Electronic Journal of Combinatorics, Dyn. Surv. Combin. (2018), Article ID: DS8.
[108] B. Zelinka, Intersection graphs of finite abelian groups, Czech. Math. J. 25 (1975), no. 2, 171–174.
[109] J. Zhao, O. Yağan, and V. Gligor, Secure k-connectivity in wireless sensor networks under an on/off channel model, 2013 IEEE International Symposium on Information Theory, 2013, pp. 2790–2794.
[110] , Connectivity in secure wireless sensor networks under transmission constraints, 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2014, pp. 1294–1301.
[111] , On the strengths of connectivity and robustness in general random intersection graphs, 53rd IEEE Conference on Decision and Control, 2014, pp. 3661–3668.