Computation of Total Vertex Irregularity Strength of Theta Graphs
Ali N. A. Koam, Ali Hasan Ahmad · IEEE Access · 2019
A total labeling$\phi: V(G)\cup E(G) \to \{1,2, {\dots }, k\}$is called avertex irregular total$k$-labelingof 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 thetotal vertex irregularity strengthof$G$, 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.