Computation of Total Vertex Irregularity Strength of Theta Graphs

A total labeling
$\phi: V(G)\cup E(G) \to \{1,2, {\dots }, k\}$
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.