Math.Comput.Sci. DOI 10.1007/s11786-015-0229-x Mathematics in Computer Science Total Irregularity Strength of Three Families of Graphs Rismawati Ramdani · A. N. M. Salman · Hilda Assiyatun · Andrea Semaniˇ cová-Fe ˇ novˇ cíková · Martin Baˇ ca Received: 20 December 2014 / Revised: 14 February 2015 / Accepted: 23 March 2015 © Springer Basel 2015 Abstract We deal with the totally irregular total labeling which is required to be at the same time vertex irregular total and also edge irregular total. The minimum k for which a graph G has a totally irregular total k -labeling is called the total irregularity strength of G. In this paper, we estimate the upper bound of the total irregularity strength of graphs and determine the exact value of the total irregularity strength for three families of graphs. Keywords Edge irregular total labeling · Vertex irregular total labeling · Totally irregular total labeling Mathematics Subject Classification Primary 05C78 1 Introduction Let G = (V , E ) be a simple and undirected graph with vertex set V and edge set E . By a labeling we mean any mapping that carries a set of graph elements to a set of numbers (usually positive integers), called labels. If the domain is the edge-set or edge-set and vertex-set, the labelings are called respectively edge labeling or total labeling. R. Ramdani · A. N. M. Salman · H. Assiyatun Department of Mathematics, Institut Teknologi Bandung, Bandung, Indonesia e-mail: rismawatiramdani@yahoo.com A. N. M. Salman e-mail: msalman@math.itb.ac.id H. Assiyatun e-mail: hilda@math.itb.ac.id R. Ramdani Department of Mathematics, The Faculty of Sciences and Technologies, Universitas Islam Negeri, Bandung, Indonesia A. Semaniˇ cová-Feˇ novˇ cíková · M. Baˇ ca (B ) Department of Applied Mathematics and Informatics, Technical University, Košice, Slovak Republic e-mail: martin.baca@tuke.sk A. Semaniˇ cová-Feˇ novˇ cíková e-mail: andrea.fenovcikova@tuke.sk