Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21282120170601Peripheral Wiener Index of a Graph43561359610.22049/cco.2017.13596ENKishori PNarayankarMangalore UniversityLokesh SBMangalore UniversityJournal Article20160528The 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<br />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.http://comb-opt.azaruniv.ac.ir/article_13596_983abceb15410e89528e5fcbb919dade.pdf