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ON NEIGHBORHOOD POLYNOMIAL OF $ G \circ H $
Keywords:
neighborhood set, neighborhood polynomialDOI:
https://doi.org/10.17654/0974165825027Abstract
A subset $S$ of $V(G)$ is a neighborhood of $G$ if $G$ can be represented as the union of the induced subgraphs of the closed neighborhoods of each vertex $v$ in $S$. Moreover, the neighborhood number denoted by $\eta(G)$ is the minimum cardinality of the neighborhood set of $G$. The neighborhood polynomial of a graph $G$ of order $m$ is defined as $N(G, x)=\sum_{i=\eta(G)}^m n(G, i) x^i$. In this paper, we obtain the neighborhood polynomial of $G \circ H$.
Received: December 17, 2024
Accepted: March 7, 2025
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