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INDEPENDENT NEIGHBORHOOD POLYNOMIAL OF THE CORONA PRODUCT OF GRAPHS
Keywords:
independent neighborhood number, independent neighborhood polynomial, corona productDOI:
https://doi.org/10.17654/0974165826004Abstract
A neighborhood set $S$ is called an independent neighborhood set of $G$ if no two vertices in $S$ are adjacent. A graph $G$ is called an $I N$-graph if $G$ has an independent neighborhood set. Then the independent neighborhood polynomial of $G$ of order $q$ is $N_i(G, x)= \sum_{j=\eta_i(G)}^q n_i(G, j) x^j$, where $n_i(G, j)$ is the number of independent neighborhood sets in $G$ of size $j$ and $\eta_i(G)$ is the minimum cardinality of an independent neighborhood set, which is called the independent neighborhood number of $G$.
In this paper, we obtain the independent neighborhood number and the independent neighborhood polynomial of the corona product of graphs.
Received: August 17, 2025
Accepted: October 28, 2025
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