Computation of Total Vertex Irregularity Strength of Theta Graphs

A total labeling phi : V(G) boolean OR E(G) -> {1, 2, ..., k} is called a vertex irregular total k-labeling of a graph G if different vertices in G have different weights. The weight of a vertex is defined as the sum of the labels of its incident edges and the label of that vertex. The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G, denoted by tvs(G). In this paper we deal with the total vertex irregularity strength of uniform theta graphs and centralized uniform theta graphs. Theta graph is a closer representation of bipolar electric or magnetic fields so labeling of various theta graphs can help the law of physics in future.