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Star complements and edge-connectivity in finite graphs

Rowlinson P (2015) Star complements and edge-connectivity in finite graphs, Linear Algebra and Its Applications, 476, pp. 124-132.

Let G be a finite graph with H as a star complement for a non-zero eigenvalue μ. Let κ'(G), δ(G) denote respectively the edge-connectivity and minimum degree of G. We show that κ'(G) is controlled by δ(G) and κ'(H). We describe the possibilities for a minimum cutset of G when μ∉{-1,0}. For such μ, we establish a relation between κ'(G) and the spectrum of H when G has a non-trivial minimum cutset E⊈E(H).

graph; connectivity; eigenvalue; star complement

AuthorsRowlinson Peter
Publication date07/2015
Publication date online19/03/2015
Date accepted by journal02/03/2015
ISSN 0024-3795

Linear Algebra and its Applications: Volume 476

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