spectrum.

In this section, we define the notion of suitably oriented graph, and using this notion we construct uncountable many matrices in $ \mathbb{T}_{G} $ having the same spectrum.

\[def.1\] Let $ G $ be a connected graph with vertex set $ V(G)=\{v_{1}, v_{2}, \dots, v_{n} \} $. Let $ T $ be a normal spanning tree of $ G $. A *suitably oriented graph* of a connected graph $ G $ with respect to $ T $ is an oriented graph, denoted by $ \overrightarrow{G_{T}} $ and is defined by assigning orientation on each edge of $ G $ as follows:\
$ \overrightarrow{e_{st}} \in E(\overrightarrow{G_{T}})$ $ v_{s} \leq v_{t} $ and $ e_{st} \in E(T) $, and\
$ \overrightarrow{e_{ts}} \in E(\overrightarrow{G_{T}})$ $ v_{s} \leq v_{t} $ and $ e_{st} \in E(G)\setminus E(T)$, where $ \leq  $ denote the tree order.

Let $ T $ be a spanning tree of a connected graph $ G $ with $ n $ vertices and $ m $ edges. Let $ C_{1}(T), C_{2}(T), \dots , C_{m-n+1}(T) $ be the fundamental cycles of $ G $ with respect to $ T $. If $ T $ is a normal spanning tree, then by definition 