On total edge irregularity strength of centralized uniform theta graphs

Let G=(V,E) be a simple connected and undirected graph. Let f:V∪E→{1,2,…,k} be a total labeling of G. The weight of an edge uv is defined by wf(uv)=f(u)+f(v)+f(uv). The labeling f is called an edge irregular total k-labeling if wf(uv)≠wf(u′v′) for any two distinct edges uv, u′v′. If G admits such a labeling, then the minimum k is called the total edge irregularity strength of G. In this paper we determine the total edge irregularity strength of centralized uniform theta graphs.