  An $n$-vertex graph whose degree set consists of exactly $n-1$ elements is
called antiregular graph. Such type of graphs are usually considered opposite
to the regular graphs. An irregularity measure ($IM$) of a connected graph $G$
is a non-negative graph invariant satisfying the property: $IM(G) = 0$ if and
only if $G$ is regular. The total irregularity of a graph $G$, denoted by
$irr_t(G)$, is defined as $irr_t(G)= \sum_{\{u,v\} \subseteq V(G)} |d_u - d_v|$
where $V(G)$ is the vertex set of $G$ and $d_u$, $d_v$ denote the degrees of
the vertices $u$, $v$, respectively. Antiregular graphs are the most nonregular
graphs according to the irregularity measure $irr_t$; however, various
non-antiregular graphs are also the most nonregular graphs with respect to this
irregularity measure. In this note, two new irregularity measures having high
discriminatory ability are devised. Only antiregular graphs are the most
nonregular graphs according to the proposed measures.
