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- W4289754452 abstract "The neighborhood polynomial of graph $G$ is the generating function for the number of vertex subsets of $G$ of which the vertices have a common neighbor in $G$. In this paper, we investigate the behavior of this polynomial under several graph operations. Specifically, we provide an explicit formula for the neighborhood polynomial of the graph obtained from a given graph $G$ by vertex attachment. We use this result to propose a recursive algorithm for the calculation of the neighborhood polynomial. Finally, we prove that the neighborhood polynomial can be found in polynomial-time in the class of $k$-degenerate graphs." @default.
- W4289754452 created "2022-08-04" @default.
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- W4289754452 date "2018-07-11" @default.
- W4289754452 modified "2023-09-26" @default.
- W4289754452 title "Graph Operations and Neighborhood Polynomials" @default.
- W4289754452 doi "https://doi.org/10.48550/arxiv.1807.03971" @default.
- W4289754452 hasPublicationYear "2018" @default.
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