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- W3199482904 abstract "The nullity of a graph is the multiplicity of zero as an eigenvalue in its adjacency spectrum. Let G be a connected graph with n vertices, maximum degree Δ and nullity η. B. Cheng et al. (2020) proved that if G is not complete bipartite and Δ≥3, then η≤(Δ−2)nΔ−1. In this paper we prove that the said inequality for η becomes equality only if Δ=3, and identify all extremal graphs that attain the equality. As an immediate by-product, some connected graphs G with Δ=3 that satisfy η=n−12 are found. We work with 0-basic subgraphs and develop a new proof technique that is based on the concepts of dual vertex and pendant-dual vertex. Some open problems are also posed." @default.
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- W3199482904 date "2022-01-01" @default.
- W3199482904 modified "2023-10-10" @default.
- W3199482904 title "On the nullity of a connected graph in terms of order and maximum degree" @default.
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- W3199482904 doi "https://doi.org/10.1016/j.laa.2021.09.015" @default.
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