A new generalization of the notion of connectivity is also given.doi:10.1016/0020-0190(88)90025-7Abdol-Hossein EsfahanianS.Louis HakimiElsevier B.V.Information Processing LettersA.H. Esfahanian, S.L. Hakimi, On
The generalized connectivity of a graph G was introduced by Chartrand et al.Let S be a nonempty set of vertices of G,and κ(S) denote the largest number of internally disjoint trees connecting S in G.Then for an integer r with 2≤r≤n,the generalized r-connectivity κ_T(G) of G ...
Clearly, κ0(G)=κ(G) for any connected non-complete graph G. So the g-extra connectivity can be viewed as a generalization of the traditional connectivity, and it can more accurately evaluate the reliability and fault tolerance for large-scale parallel processing systems accordingly. In [21]...
The generalized $k$-connectivity $\kappa_k(G)$ of a graph $G$, introduced by Hager in 1985, is a nice generalization of the classical connectivity. Recently, as a natural counterpart, we proposed the concept of generalized $k$-edge-connectivity $\lambda_k(G)$. In this paper, graphs ...
This paper concerns the generalization of SNDP into the subset-to-subset setting, namely Group EC-SNDP. We develop the framework, which yields the first non-trivial (true) approximation algorithm for Group EC-SNDP. Previously, only...
Structure fault tolerance of hypercubes and folded hypercubes Let G be a graph and T be a certain connected subgraph of G. The T-structure connectivity K(G; T) (resp. T-substructure connectivity K-s(G; T)) of G is the... E Sabir,J Meng - 《Theoretical Computer Science》 被引量: ...
from graph theory is proposed to decompose a constraint graph into a decomposition tree (abbr. D- tree). This method is a natural generalization of the methods in [17,29] which are based on tri-connectivity analysis of the constrained graph, and can solve ...
of line graph. Based on a categorical setting for persistent homology, we propose a stable pipeline for computing persistent Hochschild homology groups. This pipeline is also amenable to other homology theories; for this reason, we complement our work with a survey on homology theories of directed...
In this paper, we introduce a new combinatorial game, called a graph edge-cutting game, which is a generalization of the Shannon switching game. Graph edge-cutting game. There are two players; Snipper and Connector, where Snipper is always the first player. For a given connected graph G, ...
The path k-connectivity πk(G) of a graph G, which is a generalization of Dirac’s notion, was introduced by Hager in 1986. As a natural counterpart of path k-connectivity, the concept of path k-edge-connectivity ωk(G) of a graph G was introduced. Denote by H∘G the ...