en تخصصي Special پژوهشي Research paper Let G=(V(G),E(G)) be a connected simple undirected graph with non empty vertex set V(G) and edge set E(G). For a positive integer k, by an edge irregular total k-labeling we mean a function f : V(G)UE(G) --> {1,2,...,k} such that for each two edges ab and cd, it follows that f(a)+f(ab)+f(b) is different from f(c)+f(cd)+f(d), i.e. every two edges have distinct weights. The minimum k for which G has an edge irregular total k-labeling is called the total edge irregularity strength of graph G and denoted by tes(G). In this paper, we determine the exact value of total edge irregularity strength for staircase graphs, double staircase graphs and mirror-staircase graphs. Total edge irregularity strength, Staircase graphs, Double staircase graphs, Mirror-staircase graphs 1 13 http://ijmsi.ir/browse.php?a_code=A-10-2794-1&slc_lang=en&sid=1 Y. Susanti inielsusan@yahoo.com 10031947532846006994 10031947532846006994 Yes Dept. of Mathematics Universitas Gadjah Mada Dept. of Mathematics Universitas Gadjah Mada Y. I. Puspitasari yuliaindahp.mail@gmail.com 10031947532846006995 10031947532846006995 No Surakarta Indonesia Surakarta Indonesia H. Khotimah husnul.khotimah18@mail.ugm.ac.id 10031947532846006996 10031947532846006996 No Department of Mathematics Universitas Muhammadiyah Pringsewu Lampung Indonesia Department of Mathematics Universitas Muhammadiyah Pringsewu Lampung Indonesia