In this paper, we established the independent vertex neighborhood polynomials of complete graphs, paths, cycles, and complete bipartite graphs. In addition, we investigated these polynomials in terms of intersection points in the plane. Visual representations of graphs are presented to have closer properties of the polynomials comparing for different values of the order of the graph. Moreover, we model a social network activity as an application of this polynomial representation.

independent vertex neighborhood, graph polynomial.

Received: September 29, 2024; Accepted: November 16, 2024; Published: November 19, 2024

How to cite this article: Zuraida J. Bara, Regimar A. Rasid and Rosalio G. Artes Jr., Independent vertex neighborhood polynomials: behavior of graphs and some applications, Advances and Applications in Discrete Mathematics 42(1) (2025), 47-54. https://doi.org/10.17654/0974165825003

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