181 research outputs found
Matching Preclusion and Conditional Matching Preclusion Problems for Twisted Cubes
The matching preclusion number of a graph is the minimum
number of edges whose deletion results in a graph that has neither
perfect matchings nor almost-perfect matchings. For many interconnection
networks, the optimal sets are precisely those induced by a
single vertex. Recently, the conditional matching preclusion number
of a graph was introduced to look for obstruction sets beyond those
induced by a single vertex. It is defined to be the minimum number
of edges whose deletion results in a graph with no isolated vertices
that has neither perfect matchings nor almost-perfect matchings. In
this paper, we find the matching preclusion number and the conditional matching preclusion number for twisted cubes, an improved
version of the well-known hypercube. Moreover, we also classify all
the optimal matching preclusion sets
Super edge-connectivity and matching preclusion of data center networks
Edge-connectivity is a classic measure for reliability of a network in the
presence of edge failures. -restricted edge-connectivity is one of the
refined indicators for fault tolerance of large networks. Matching preclusion
and conditional matching preclusion are two important measures for the
robustness of networks in edge fault scenario. In this paper, we show that the
DCell network is super- for and ,
super- for and , or and , and
super- for and . Moreover, as an application of
-restricted edge-connectivity, we study the matching preclusion number and
conditional matching preclusion number, and characterize the corresponding
optimal solutions of . In particular, we have shown that is
isomorphic to the -star graph for .Comment: 20 pages, 1 figur
Generalized Matching Preclusion in Bipartite Graphs
The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal such sets are precisely sets of edges incident to a single vertex. The conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond these, and it is defined as the minimum number of edges whose deletion results in a graph with neither isolated vertices nor perfect matchings. In this paper we generalize this concept to get a hierarchy of stronger matching preclusion properties in bipartite graphs, and completely characterize such properties of complete bipartite graphs and hypercubes
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