TRIREGULAR GRAPHS WHOSE ENERGY EXCEEDS THE NUMBER OF VERTICES Snjeˇ zana Majstorovi´ c, a Antoaneta Klobuˇ car a and Ivan Gutman b b Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, HR–31000 Osijek, Croatia e-mail: antoaneta.klobucar@os.htnet.hr , smajstor@mathos.hr a Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia e-mail: gutman@kg.ac.yu (Received July 23, 2008) Abstract A graph is said to be triregular if its vertex degrees assume exactly three different values. The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of G . Conditions are established under which the inequality E(G) >n is obeyed for connected n-vertex acyclic, unicyclic, and bicyclic triregular graphs. MATCH Communications in Mathematical and in Computer Chemistry MATCH Commun. Math. Comput. Chem. 62 (2009) 509-524 ISSN 0340 - 6253