University of Isfahan Transactions on Combinatorics 2251-8657 11 2 2022 06 01 Peripheral Hosoya polynomial of composite graphs 63 76 26025 10.22108/toc.2021.127151.1813 EN Anteneh Alemu Ali Department of Mathematics, Mangalore University, Mangalore-574199, India Kishori P. Narayankar Department of Mathematics, Mangalore University, Mangalore-574199, India Journal Article 2021 01 23 Peripheral Hosoya polynomial of a graph $G$ is defined as‎,<br />‎ \begin{align*}‎<br />‎ &PH(G,\lambda)=\sum_{k\geq 1}d_P(G,k)\lambda^k,\\‎<br />‎ \text{where $d_P(G,k)$ is the number} &\text{ of pairs of peripheral vertices at distance $k$ in $G$.}‎<br />‎ \end{align*}‎<br />Peripheral Hosoya polynomial of composite graphs viz.‎, ‎$G_1\times G_2$ the Cartesian product‎, ‎$G_1+G_2$ the join‎, ‎$G_1[G_2]$ the composition‎, ‎$G_1\circ G_2$ the corona and $G_1\{G_2\}$ the cluster of arbitrary connected graphs $G_1$ and $G_2$ are computed and their peripheral Wiener indices are stated as immediate consequences‎. https://toc.ui.ac.ir/article_26025_3ff14793f03f06efb256958566913365.pdf