Restricted Edge Connectivity of Regular Graphs
نویسنده
چکیده
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. It is proved in this paper that : every k regular connected graph G with k ≥2 and | G| ≥4 is maximal restricted edge connected if k > | G| Π2. It is also exemplified that the lower bound of k in this proposition cannot be improved to some extent .
منابع مشابه
On restricted edge connectivity of regular Cartesian product graphs
Explicit expressions of the restricted edge connectivity of the Cartesian product of regular graphs are presented; some sufficient conditions for regular Cartesian product graphs to be maximally or super restricted edge connected are obtained as a result.
متن کاملOn the edge-connectivity of C_4-free graphs
Let $G$ be a connected graph of order $n$ and minimum degree $delta(G)$.The edge-connectivity $lambda(G)$ of $G$ is the minimum numberof edges whose removal renders $G$ disconnected. It is well-known that$lambda(G) leq delta(G)$,and if $lambda(G)=delta(G)$, then$G$ is said to be maximally edge-connected. A classical resultby Chartrand gives the sufficient condition $delta(G) geq frac{n-1}{2}$fo...
متن کاملSufficient conditions for maximally edge-connected and super-edge-connected
Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...
متن کاملOn a kind of restricted edge connectivity of graphs
Let G=(V; E) be a connected graph and S ⊂E. S is said to be a m-restricted edge cut (m-RC) if G − S is disconnected and each component contains at least m vertices. The m-restricted edge connectivity (G) is the minimum size of all m-RCs in G. Based on the fact that (G)6 3(G), where m(G)=min{!(X ): X ⊂V; |X |=m and G[X ] is connected} (!(X ) denotes the number of edges with one end vertex in X a...
متن کاملThe k-restricted edge-connectivity of a product of graphs
This work deals with a generalization of the Cartesian product of graphs, the product graph Gm ∗Gp introduced by Bermond et al. [J.C. Bermond, C. Delorme, G. Farhi, Large graphs with givendegree anddiameter II, J. Combin. Theory, Series B 36 (1984), 32–48]. The connectivity of these product graphs is approached by studying the k-restricted edge-connectivity, which is defined as the minimum numb...
متن کامل