On The Total Irregularity Strength of Regular Graphs
Daftar Isi:
- Let G = (V, E) be a graph. A total labeling f: V ∪ E → {1, 2, ⋯ , k} iscalled a totally irregular total k-labeling of G if every two distinct vertices x andy in V satisfy wf(x) ≠ wf(y) and every two distinct edges x1x2 and y1y2 in Esatisfy wf(x1x2) ≠ wf(y1y2), where wf(x) = f(x) + Σxz∈E(G) f(xz) andwf(x1x2) = f(x1) + f(x1x2) + f(x2). The minimum k for which a graph G hasa 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 totalirregularity 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.