Various empty carbon fullerenes (Cn) with different carbon atoms have been obtained and investigated.Cephalosporin antibiotics and its derivatives have important medicinal properties. The b-lactam class of antibiotics has a broad spectrum of antimicrobial properties.Their antibacterial and pharmacokinetic properties have wide therapeutic applications. Topological indices have been successfully used to construct effective and useful mathematical methods to establish clear relationships between structural data and the physical properties of these materials. In this study, the number of carbon atoms in fullerenes was used as an index to establish a relationship between the structures of cefadroxil, cefepime, cephalexin, cefotaxime, cefoperazone and ceftriaxone (b-lactam antibiotics) and fullerenes (Cn, n=60, 70, 76, 82 and 86), which create [cefadroxil] Cn, [cefepime] Cn, [cephalexin] Cn, [cefotaxime] Cn, [cefoperazone]...