منابع مشابه
On critically k-edge-connected graphs
Let G be a simple graph on n vertices having edge-connectivity /(.' (G) > a and minimum degree o(G) We say G is k-critical if /(.' (G) = k and /(.' (G e) < k for every edge e of G. In this paper we prove that a k-critical graph has 1<' (G) o(G). We descri be a number of classes of k-cri tical graphs and consider the problem of determining the edge-maximal ones.
متن کاملThe characterization of edge-maximal critically k-edge connected graphs
Let G be a simple graph on n vertices having edge-connectivity 1(' (G) > O. We say G is k-critical if 1(' (G) :::: k and 1(1 (G-e) < k for every edge e of G. We denote by ~(n,k) the set of all k-critical graphs on n vertices. In this paper we prove that the maximum number of edges of a graph G in ~(n,k) to be: k(n-k) if n ~ 3k; and L ~ (n+k)2 J. if k + 1 s n < 3k. Further, we characterise the e...
متن کاملMinimally (k, k-1)-edge-connected graphs
For an interger l > 1, the l-edge-connectivity λl(G) of G is defined to be the smallest number of edges whose removal leaves a graph with at least l components, if |V (G)| ≥ l; and λl(G) = |V (G)| if |V (G)| ≤ l. A graph G is (k, l)-edge-connected if the l-edge-connectivity of G is at least k. A sufficient and necessary condition for G to be minimally (k, k − 1)-edgeconnected is obtained in the...
متن کامل(t, k)-Shredders in k-Connected Graphs
Let t, k be integers with t ≥ 3 and k ≥ 1. For a graph G, a subset S of V (G) with cardinality k is called a (t, k)-shredder if G−S consists of t or more components. In this paper, we show that if t ≥ 3, 2(t−1) ≤ k ≤ 3t−5 and G is a k-connected graph of order at least k, then the number of (t, k)-shredders of G is less than or equal to ((2t−1)(|V (G)|−f(|V (G)|)))/(2(t−1)), where f(n) denotes t...
متن کاملON GENERALIZED k-DIAMETER OF k-REGULAR k-CONNECTED GRAPHS
In this paper, motivated by the study of the wide diameter and the Rabin number of graphs, we define the generalized k-diameter of k-connected graphs, and show that every k-regular k-connected graph on n vertices has the generalized k-diameter at most n/2 and this upper bound cannot be improved when n = 4k − 6 + i(2k − 4).
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1987
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90114-2