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DOUBLY INDEPENDENT NEIGHBORHOOD POLYNOMIALS OF GRAPHS
Keywords:
independent set, neighborhood system, doubly independent neighborhood polynomialDOI:
https://doi.org/10.17654/0972087125021Abstract
In this paper, we introduce the concept of doubly independent neighborhood polynomial of a graph. This polynomial represents the number of independent sets in a graph with corresponding maximal independent set in the neighborhood system. For an increasing sequence $\left\langle r_i\right\rangle_{i=1}^q$ of natural numbers, we establish the doubly independent neighborhood polynomial of $K_{r_1, r_2}, \ldots, r_q$.
Received: May 1, 2025
Revised: May 29, 2025
Accepted: June 2, 2025
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