Geodesic
Reconstructing Surface Triangulations by Their Intersection Matrices
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 3, pp. 483-491

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The intersection matrix of a simplicial complex has entries equal to the rank of the intersecction of its facets. We prove that this matrix is enough to define up to isomorphism a triangulation of a surface.
Keywords: triangulated surface, isomorphism, intersection matrix 
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     author = {Arocha, Jorge L. and Bracho, Javier and Garc{\'\i}a-Col{\'\i}n, Natalia and Hubard, Isabel},
     title = {Reconstructing {Surface} {Triangulations} by {Their} {Intersection} {Matrices}},
     journal = {Discussiones Mathematicae. Graph Theory},
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Arocha, Jorge L.; Bracho, Javier; García-Colín, Natalia; Hubard, Isabel. Reconstructing Surface Triangulations by Their Intersection Matrices. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 3, pp. 483-491. http://geodesic.mathdoc.fr/item/DMGT_2015_35_3_a7/