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Suppose that G is an undirected graph, and that H is a spanning subgraph of G c whose edges induce a subgraph on p vertices. We consider the expression α(G∪H)− α(G), where α denotes the algebraic connectivity. Specifically, we provide upper and lower bounds on α(G ∪ H) − α(G) in terms of p, and characterise the corresponding equality cases. We also discuss(More)
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