// 2–edge connectivity in a graph intmain() { // vector of graph edges vector<Edge>edges={ {0,2},{1,2},{2,3},{2,4},{3,4},{3,5} }; // total number of nodes in the graph (0 to 6) intn=10; // build a graph from the given edges ...
For $k=3$, we study the relation between the edge-connectivity and the generalized 3-edge-connectivity of a graph. Upper and lower bounds of $\\\lambda_3(G)$ for a graph $G$ in terms of the edge-connectivity $\\\lambda$ of $G$ are obtained, that is, $\\\frac{3\\\lambda-2...
exactly two connected components each containing at least k vertices. This graph invariant, which can be seen as a generalization of a minimum edge-cut, has been extensively studied from a combinatorial point of view. However, very little is known about the complexity of computing λ k ( G )...
On the connectivity and restricted edge-connectivity of 3-arc graphs Let G denote the symmetric digraph of a graph G. A 3-arc is a 4-tuple (y,a,b,x) of vertices such that both (y,a,b) and (a,b,x) are paths of length 2 in G. ... C Balbuena,P García-Vázquez,LP Montejan...
摘要: Sufficient conditions for the equality of edge-connectivity and minimum degree of a graph or a bipartite graph are presented. Also previously known conditions are surveyed. Key words. Graph, bipartite graph, edge-connectivity, minimum degree, distance....
Conjecture/Question: What is the largest cyclic edge-connectivity of a 5 -connected planar graph? The answer is at least 10 and at most 13 . Definitions/Background/motivation: A graph is cyclically k -edge-connected if at least k edges must be removed to disconnect it into two components ...
Also, the edge-vertex degree of the edge e = uv, d v G (e), equals to the number of vertices of the union of the open neighborhood of u and v. In this paper, the vertex-edge connectivity index, φ v , and the edge-vertex connectivity index, φ e , of a graph G were ...
An edge set S of a connected graph G is a k-extra edge cut, if G - S is no longer connected, and each component of G - S has at least k vertices. The cardinality of a minimum k-extra edge cut, denoted by λ k ( G ), is the k-extra edge connectivity of G. The kth isop...
Super Restricted Edge Connectivity of Regular Graphs An edge cut of a connected graph is called restricted if it separates this graph into components each having order at least 2; a graph G is super restricte... JF Zhang - 《Graphs & Combinatorics》 被引量: 0发表: 2005年 加载更多来源...
Summary: This paper considers the concept of restricted edge-connectivity, and relates that to the edge-degree of a connected graph. The author gives some ... JM Xu,KL Xu - 《Discrete Mathematics》 被引量: 321发表: 2002年 On connectivity of the Cartesian product of two graphs In this pap...