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\section*{Addendum}
Recently we have been pointed out that a strengthening of Theorem 7 can be derived from a result showed by Balister \emph{et al.}~\cite{BGLS07}. In their paper the authors study the notion of adjacent vertex-distinguishing edge-coloring, which is a proper edge-coloring such that for each pair of adjacent vertices $u$ and $v$, the set of colors incident to $u$ is not equal to the set of colors incident to $v$.
 The minimum number of colors required to obtain an adjacent vertex distinguishing edge-coloring of $G$ is denoted $\chi^\prime_a(G)$.

Note that when the graph is $\Delta$-regular, a $(\Delta-1)$-intersection $(\Delta+1)$-edge coloring is equivalent to an adjacent vertex-distinguishing edge-coloring. In the context of subcubic graphs, Balister \emph{et al.} proved the following result:

\begin{theorem}[Balister \emph{et al.} \cite{BGLS07}]
Let $G$ be a subcubic graph with no isolated edge, then $\chi^\prime_a(G)\le5$.
\end{theorem}

From this result a strengthening of Theorem 7 of our paper follows easily :

\begin{corollary}
Let $G$ be a subcubic graph. Then $\chik{2}(G)\leq 5$.
\end{corollary}

Moreover, as mentioned in Section~2 of our paper, there are subcubic graphs with $\chik{2}(G) = 5$ and thus the result of the above corollary is tight.




\begin{thebibliography}{10}
\bibitem{BGLS07}
P.N. Balister, E. Győri, J. Lehel and R.H. Schelp.
\newblock Adjacent vertex-distinguishing edge-colorings.
\newblock {\em SIAM Journal on Discrete Mathematics}, 21(1):237--250, 2007.
\end{thebibliography}

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