Edge Connectivity of a Graph Edge connectivityof a graph refers to the minimum number of edges that must be removed to disconnect the graph. In other words, it measures how many edges must be removed to make the graph disconnected, or to separate it into two or more disconnected components....
The k-restricted edge-connectivity of a graph G , denoted by λ k (G) λ k ( G ) mathContainer Loading Mathjax , is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least k vertices. This graph invariant, ...
// 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 ...
The unweighted k-edge-connectivity augmentation problem (kECA for short) is deffned by “Given a σ-edge-connected graph G = (V,E), find an edge set E’ of minimum cardinality such that G’ = (V,E∪ E’) is (σ+δ)-edge-connected and...
摘要 The local-restricted-edge-connectivity lambda'(e, f) of two nonadjacent edges e and f in graph G is the maximum number of edge-disjoint e-f paths in G. It is clear that lambda'(G) = min{lambda'(e, f)vertical bar e and f are nonadjacent edges in G}, and lambda'(e, f...
Simplicity-preserving augmentation of the edge-connectivity of a graph The main technical tool is a simplicity-preserving edge splitting-off operation, which is used to "short-cut" vertices with high degree while maintaining ... S Taoka - 《Tech.rep.of Ieice of Japan》 被引量: 0发表: 1994...
Definition 1.1 Game edge-connectivity The game edge-connectivity of a graph G, denoted by λgame(G), is the smallest m such that Snipper can make G be disconnected within m moves of Snipper for any play of Connector in the graph edge-cutting game. We define λgame(G)=∞ if Connector ...
Also, the edge-vertex degree of the edge e = uv, dvG(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, v, and the edge-vertex connectivity index, e, of a graph G were introduced. These are...
A 1.5 approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2 Information Processing Letters, 111 (6) (2011), pp. 296-300 View PDFView articleView in ScopusGoogle Scholar [4] G.N. Fredrickson, J. Jájá On the relationship between the biconnectivity augmentation and ...
Let $G$ be a graph and there exist at least two non-empty disjoint proper subsets $V_{1},V_{2}\subseteq V=V(G)$ such that edge connectivity $\kappa'(G)=e(V_{i},V\backslash V_{i})$ for $1\leq i \leq 2$ and $V\setminus(V_{1} \cup V_{2})eq \phi,$ then this ...