Eigenvalues and edge-connectivity of regular graphs
نویسندگان
چکیده
منابع مشابه
Eigenvalues and edge-connectivity of regular graphs
In this paper, we show that if the second largest eigenvalue of a d-regular graph is less than d − 2(k−1) d+1 , then the graph is k-edge-connected. When k is 2 or 3, we prove stronger results. Let ρ(d) denote the largest root of x3 − (d− 3)x2 − (3d− 2)x− 2 = 0. We show that if the second largest eigenvalue of a d-regular graph G is less than ρ(d), then G is 2-edge-connected and we prove that if...
متن کاملEdge-Connectivity, Eigenvalues, and Matchings in Regular Graphs
In this paper, we study the relationship between eigenvalues and the existence of certain subgraphs in regular graphs. We give a condition on an appropriate eigenvalue that guarantees a lower bound for the matching number of a t-edge-connected d-regular graph, when t ≤ d − 2. This work extends some classical results of von Baebler and Berge and more recent work of Cioabă, Gregory, and Haemers. ...
متن کاملEdge-Disjoint Spanning Trees, Edge Connectivity, and Eigenvalues in Graphs
Let λ2(G) and τ (G) denote the second largest eigenvalue and the maximum number of edge-disjoint spanning trees of a graph G, respectively. Motivated by a question of Seymour on the relationship between eigenvalues of a graph G and bounds of τ (G), Cioabă and Wong conjectured that for any integers d , k ≥ 2 and a d -regular graph G, if λ2(G) < d − 2k−1 d+1 , then τ (G) ≥ k. They proved the conj...
متن کاملMatching and edge-connectivity in regular graphs
Henning and Yeo proved a lower bound for the minimum size of a maximum matching in a connected k-regular graphs with n vertices; it is sharp infinitely often. In an earlier paper, we characterized when equality holds. In this paper, we prove a lower bound for the minimum size of a maximum matching in an l-edge-connected k-regular graph with n vertices, for l ≥ 2 and k ≥ 4. Again it is sharp for...
متن کاملRestricted Edge Connectivity of Regular Graphs
An edge cut that separates the connected graph into components with order at least two is restricted edge cut. The cardinality of minimum restricted edge cut is restricted edge connectivity. Denote byλ′ ( G) the restricted edge connectivity , then λ′( G) ≤ξ( G) where ξ( G) is the minimum edge degree. G is called maximal restricted edge connected if the equality in the previous inequality holds....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2010
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.08.029