  For a given simple graph $G$, the energy of $G$, denoted by $\mathcal
{E}(G)$, is defined as the sum of the absolute values of all eigenvalues of its
adjacency matrix, which was defined by I. Gutman. The problem on determining
the maximal energy tends to be complicated for a given class of graphs. There
are many approaches on the maximal energy of trees, unicyclic graphs and
bicyclic graphs, respectively. Let $P^{6,6,6}_n$ denote the graph with $n\geq
20$ vertices obtained from three copies of $C_6$ and a path $P_{n-18}$ by
adding a single edge between each of two copies of $C_6$ to one endpoint of the
path and a single edge from the third $C_6$ to the other endpoint of the
$P_{n-18}$. Very recently, Aouchiche et al. [M. Aouchiche, G. Caporossi, P.
Hansen, Open problems on graph eigenvalues studied with AutoGraphiX, {\it
Europ. J. Comput. Optim.} {\bf 1}(2013), 181--199] put forward the following
conjecture: Let $G$ be a tricyclic graphs on $n$ vertices with $n=20$ or
$n\geq22$, then $\mathcal{E}(G)\leq \mathcal{E}(P_{n}^{6,6,6})$ with equality
if and only if $G\cong P_{n}^{6,6,6}$. Let $G(n;a,b,k)$ denote the set of all
connected bipartite tricyclic graphs on $n$ vertices with three vertex-disjoint
cycles $C_{a}$, $C_{b}$ and $C_{k}$, where $n\geq 20$. In this paper, we try to
prove that the conjecture is true for graphs in the class $G\in G(n;a,b,k)$,
but as a consequence we can only show that this is true for most of the graphs
in the class except for 9 families of such graphs.
