Peripheral Hosoya polynomial of composite graphs

Document Type : Research Paper


Department of Mathematics, Mangalore University, Mangalore-574199, India


Peripheral Hosoya polynomial of a graph $G$ is defined as‎,
‎ \begin{align*}‎
‎ &PH(G,\lambda)=\sum_{k\geq 1}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.‎, ‎$G_1\times G_2$ 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.


Main Subjects

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  • Receive Date: 23 January 2021
  • Revise Date: 05 October 2021
  • Accept Date: 12 October 2021
  • Published Online: 01 June 2022