Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599114 | Linear Algebra and its Applications | 2015 | 9 Pages |
Abstract
Let G be a finite graph with H as a star complement for a non-zero eigenvalue μ . Let κ′(G)κ′(G), δ(G)δ(G) denote respectively the edge-connectivity and minimum degree of G . We show that κ′(G)κ′(G) is controlled by δ(G)δ(G) and κ′(H)κ′(H). We describe the possibilities for a minimum cutset of G when μ∉{−1,0}μ∉{−1,0}. For such μ , we establish a relation between κ′(G)κ′(G) and the spectrum of H when G has a non-trivial minimum cutset E⊈E(H)E⊈E(H).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Peter Rowlinson,