Document Type : Original paper
The eccentricity of a vertex $v$ is the maximum distance between $v$ and any
other vertex. A vertex with maximum eccentricity is called a peripheral vertex.
The peripheral Wiener index $ PW(G)$ of a graph $G$ is defined as the sum of
the distances between all pairs of peripheral vertices of $G.$ In this paper, we
initiate the study of the peripheral Wiener index and we investigate its basic
properties. In particular, we determine the peripheral Wiener index of the
cartesian product of two graphs and trees.