When the Comaximal Graph of a Lattice is Toroidal

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Afkhami, Mojgan (Department of Mathematics, University of Neyshabur) ;
Javaheri, Khadijeh Ahmad (Department of Pure Mathematics, Internatinal Compus of Ferdowsi University of Mashhad) ;
Khashyarmanesh, Kazem (Department of Pure Mathematics, Internatinal Compus of Ferdowsi University of Mashhad)

In this paper we investigate the toroidality of the comaximal graph of a finite lattice.

M. Afkhami and K. Khashyarmanesh, The comaximal graph of a lattice, Bull. Malays. Math. Sci. Soc., 37(2014), 261-269.
J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, American Elsevier, New York, 1976.
A. Bouchet, Orientable and nonorientable genus of the complete bipartite graph, J. Combin. Theory Ser. B 24(1978), 24-33.
F. Harary, P. C. Kainen, A. J. Schwenk and A. T. White, A maximal toroidal graph which is not a triangulation, Math.Scand. 33(1973), 108-112. https://doi.org/10.7146/math.scand.a-11476
A. L. Hlavacek, 9-vertex irreducible graphs for the torus, PhD. thesis, The university of Ohio State, 1997.
H. R. Maimani, M. Salimi, A. Sattari and S. Yassemi, Comaximal graph of commutative rings, J. Algebra 319(2008), 1801-1808. https://doi.org/10.1016/j.jalgebra.2007.02.003
J. B. Nation, Notes on Lattice Theory, Cambridge studies in advanced mathematics, Vol. 60, Cambridge University Press, Cambridge, 1998.
G. Ringel, Map Color Theorem, Springer-Verlag, New York/Heidelberg, 1974.
P. K. Sharma, S. M. Bhatwadekar, A note on graphical representation of rings, J. Algebra 176(1995), 124-127. https://doi.org/10.1006/jabr.1995.1236
H. J. Wang, Graphs associated to co-maximal ideals of commutative rings, J. Algebra 320(2008), 2917-2933. https://doi.org/10.1016/j.jalgebra.2008.06.020
D. Zeps, Forbidden minors for projective plane are free-toroidal or non-toroidal, IUUK-CE-ITI series (2009).