Corpus ID: 237940121

Algebraic connectivity of some supergraphs of a graph

@inproceedings{Afshari2021AlgebraicCO,
  title={Algebraic connectivity of some supergraphs of a graph},
  author={Bahareh Afshari},
  year={2021}
}
The algebraic connectivity λ2(G) of a (weighted) graph G is the second smallest eigenvalue of its Laplacian matrix. Let G = (V,E) be an unweighted graph on n vertices and Ni be the set of all neighbors of vi ∈ V . Let G′ be the graph obtained from G by giving the weight 1 n to the pairs of vertices with distance at least 3 in G. Then λ2(G ′) ≥ 1. As a corollary of this result, we get λ2(G) ≥ 1 n λ2(G ), and λ2(G) + λ2(G) ≥ 1, where G is the second power of G and G is its complement. For an… Expand

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