On the total irregularity strength of regular graphs

Let g = (v,e) be a graph. a total labeling f: v ∪ e → {1,2,⋯,k} is called a totally irregular total k-labeling of g if every two distinct vertices x and y in v satisfy wf(x) ≠ wf(y) and every two distinct edges x1x2 and y1y2 in e satisfy wf(x1x2) ≠ (x1x2),where wf(x) = f(x) + σxz∈e(g) f(x,z) and wf(x1x2) =f(x1) + f(x1x2) + f(x2). the minimum k for which a graph g has a totally irregular total k-labeling is called the total irregularity strength of g,denoted by ts(g). in this paper,we consider an upper bound on the total irregularity strength of m copies of a regular graph. besides that,we give a dual labeling of a totally irregular total k-labeling of a regular graph and we consider the total irregularity strength of m copies of a path on two vertices,m copies of a cycle,and m copies of a prism cn□p2. © 2015 published by itb journal publisher.