J Math Chem (2013) 51:2354–2360 DOI 10.1007/s10910-013-0215-y ORIGINAL PAPER Three-dimensional chiral objects and their star graph representations Ottilia Fülöp · Béla Barabás Received: 26 April 2013 / Accepted: 18 June 2013 / Published online: 6 August 2013 © Springer Science+Business Media New York 2013 Abstract Planar chirality properties can be analysed using n-polyominoes and graphs. In this paper we study graph representations of three-dimensional chiral objects and discuss the generalization of planar case. We show that graph representations of three- dimensional chiral objects can be star graphs. Keywords Chirality · 3D Jordan property · Graph representations 1 Introduction Chirality in the ordinary, three-dimensional space plays a key role in many fields of the natural sciences, especially in biology, chemistry, pharmacology and medical cosme- tology. In chemistry, chirality is a property of molecules having a non superimposable mirror image. In mathematics, chirality of an object S in the three-dimensional space R 3 means, that it cannot produce a perfect overlap with its mirror image S ♦ within R 3 . Otherwise S is said to be achiral in R 3 . The simplest approach of chirality is to say that a 3D object (or a molecule) is either chiral or achiral. One can think that there is no other possibility. On the other hand a few scientists recognized that it is possible to measure the degree of chirality. For example Frank Harary, R.W. Robinson, P.G. Mezey, A.I. Kitaigorodski, K. Mislow, O. Fülöp · B. Barabás (B ) Institute of Mathematics, Budapest University of Technology and Economics, Egry J. u. 1., Budapest 1111, Hungary e-mail: belab@math.bme.hu O. Fülöp e-mail: otti@math.bme.hu 123