首页|On the nullity of a connected graph in terms of order and maximum degree
On the nullity of a connected graph in terms of order and maximum degree
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NSTL
Elsevier
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 [Formula presented]. 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 [Formula presented] 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.
0-Basic subgraphDual vertexInduced subgraphNullity of a graphPendant K2 deletionPendant-dual vertexRank
Cheng B.、Liu M.、Tam B.-S.
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Department of Applied Mathematics School of Mathematics and Statistics Guangdong University of Foreign Studies
Department of Mathematics College of Mathematics and Informatics South China Agricultural University
NSTL
Elsevier
