Convex Independent Neighborhood Polynomial of Some Special Graphs (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we introduced the notion of convex independent neighborhood polynomial for a graph. We further explored the convex independent neighborhood polynomial for some special graphs such as paths, cycles, complete graphs, and star graphs. We generated these polynomials by counting the number of convex subsets of a graph with corresponding maximum independent set in the neighborhood system.
Keywords: convex sets; convex subgraph; independent neighborhood system; independent set; convex independent neighborhood polynomial