Anteneh Ali - Department of Mathematics, Mangalore University, Mangalore-۵۷۴۱۹۹, India
Kishori Narayankar - Department of Mathematics, Mangalore University, Mangalore-۵۷۴۱۹۹, India

Peripheral Hosoya polynomial of a graph G is defined as‎,‎ \begin{align*}‎‎ &PH(G,\lambda)=\sum_{k\geq ۱}d_P(G,k)\lambda^k,\\‎‎ \text{where d_P(G,k) is the number} &\text{ of pairs of peripheral vertices at distance k in G.}‎‎ \end{align*}‎Peripheral Hosoya polynomial of composite graphs viz.‎, ‎G_۱\times G_۲ the Cartesian product‎, ‎G_۱+G_۲ the join‎, ‎G_۱[G_۲] the composition‎, ‎G_۱\circ G_۲ the corona and G_۱\{G_۲\} the cluster of arbitrary connected graphs G_۱ and G_۲ are computed and their peripheral Wiener indices are stated as immediate consequences‎.

‎Peripheral Hosoya polynomial‎, ‎Composite graph‎, ‎Peripheral Wiener index‎, ‎Hosoya polynomial‎, ‎Wiener Index