Abstract: A \emph{simple geodesic path cover} $\mathcal{SGPC}$ of a graph $G$ is a decomposition of $G$ into shortest paths such that any two members of the decomposition share at most one vertex. The minimum cardinality of a simple geodesic path cover of $G$ is called the \emph{simple geodesic path covering number} of $G$ and is denoted by $\pi_{sg}(G)$. This concept was introduced in \cite{ssp}. This paper
further studies this concept.

Keywords: Simple geodesic path cover, Helly property.

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