  Total irregularity of a simple undirected graph $G$ is defined to be
$irr_t(G) = \frac{1}{2}\sum\limits_{u, v \in V(G)}|d(u) - d(v)|$. See Abdo and
Dimitrov [2]. We allocate the \emph{Fibonacci weight,} $f_i$ to a vertex $v_j$
of a simple connected graph, if and only if $d(v_j) = i$ and define the
\emph{total fibonaccian irregularity} or $f_t-irregularity$ denoted $firr_t(G)$
for brevity, as: $firr_t(G) =
\sum\limits_{i=1}^{n-1}\sum\limits_{j=i+1}^{n}|f_i - f_j|.$ The concept of an
\emph{edge-joint} is also introduced to be the simple undirected graph obtained
from two simple undirected graphs $G$ and $H$ by linking the edge $vu_{v \in
V(G), u \in V(H)}$. This paper presents results for the undirected underlying
graphs of Jaco Graphs, $J_n(x)$. Finally we pose an open problem with regards
to $firr_t^\pm(G).$
