AUSTRALASIAN JOURNAL OF COMBINATORICS Volume 59(1) (2014), Pages 98–106 Irregular total labeling of disjoint union of prisms and cycles Ali Ahmad College of Computer Science & Information Systems Jazan University, Jazan Saudi Arabia ahmadsms@gmail.com Martin Ba ˇ ca ∗ Department of Applied Mathematics and Informatics Technical University, Koˇ sice Slovakia martin.baca@tuke.sk Muhammad Kamran Siddiqui Abdus Salam School of Mathematical Sciences GC University, Lahore Pakistan kamransiddiqui75@gmail.com Abstract We investigate two modifications of the well-known irregularity strength of graphs, namely, a total edge irregularity strength and a total vertex irregularity strength. Recently the bounds and precise values for some families of graphs concerning these parameters have been determined. In this paper, we determine the exact value of the total edge (vertex) irregularity strength for the disjoint union of prisms and the total edge (vertex) irregularity strength for the disjoint union of cycles. * Corresponding author. Second address: Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.