Star Complements and Edge-connectivity in Finite Graphs
نویسنده
چکیده
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 6∈ {−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 6⊆ E(H). AMS Classification: 05C50
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