254 research outputs found
Steiner Distance in Product Networks
For a connected graph of order at least and , the
\emph{Steiner distance} among the vertices of is the minimum size
among all connected subgraphs whose vertex sets contain . Let and be
two integers with . Then the \emph{Steiner -eccentricity
} of a vertex of is defined by . Furthermore, the
\emph{Steiner -diameter} of is . In this paper, we investigate the Steiner distance and Steiner
-diameter of Cartesian and lexicographical product graphs. Also, we study
the Steiner -diameter of some networks.Comment: 29 pages, 4 figure
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
Conditional Strong Matching Preclusion of the Alternating Group Graph
The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. Park and Ihm introduced the problem of strong matching preclusion under the condition that no isolated vertex is created as a result of faults. In this paper, we find the conditional strong matching preclusion number for the -dimensional alternating group graph
The Conditional Strong Matching Preclusion of Augmented Cubes
The strong matching preclusion is a measure for the robustness of interconnection networks in the presence of node and/or link failures. However, in the case of random link and/or node failures, it is unlikely to find all the faults incident and/or adjacent to the same vertex. This motivates Park et al. to introduce the conditional strong matching preclusion of a graph. In this paper we consider the conditional strong matching preclusion problem of the augmented cube , which is a variation of the hypercube that possesses favorable properties
Matching Preclusion of the Generalized Petersen Graph
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 with no perfect matchings. In this paper we determine the matching preclusion number for the generalized Petersen graph and classify the optimal sets
Fault diagnosability of regular graphs
An interconnection network\u27s diagnosability is an important measure of its self-diagnostic capability. In 2012, Peng et al. proposed a measure for fault diagnosis of the network, namely, the -good-neighbor conditional diagnosability, which requires that every fault-free node has at least fault-free neighbors. There are two well-known diagnostic models, PMC model and MM* model. The {\it -good-neighbor diagnosability} under the PMC (resp. MM*) model of a graph , denoted by (resp. ), is the maximum value of such that is -good-neighbor -diagnosable under the PMC (resp. MM*) model. In this paper, we study the -good-neighbor diagnosability of some general -regular -connected graphs under the PMC model and the MM* model. The main result with some acceptable conditions is obtained, where is the girth of . Furthermore, the following new results under the two models are obtained: for the hierarchical star network , for the split-star networks and for the Cayley graph generated by the -tree
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