In this paper, we introduce a new graph polynomial called the  biclique neighborhood polynomial of a graph. This counts the number of bicliques in a graph with corresponding cardinality of the neighborhood system. We obtain results on the biclique neighborhood polynomials of some structured graphs.

biclique, neighborhood system, biclique neighborhood polynomial.

Received: July 7, 2024; Accepted: August 20, 2024; Published: September 27, 2024

How to cite this article: Shiena Mae B. Lumpayao and Regimar A. Rasid, Biclique neighborhood polynomials of graphs, Advances and Applications in Discrete Mathematics 41(7) (2024), 581-588. https://doi.org/10.17654/0974165824038

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