Strong matching preclusion number of graphs

Mao, Yaping; Wang, Zhao; Cheng, Eddie; Melekian, Christopher

doi:10.1016/j.tcs.2017.12.035

Cited by 23 publications

(5 citation statements)

References 21 publications

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“…The strong matching preclusion number (SMP number for short) of G, denoted by smp(G), is the minimum number of SMP sets of G. A SMP set is optimal if |F| = smp(G). The problem of strong matching preclusion set was proposed by Park and Ihm (Park & Ihm) and further studied by (Mao, Wang, Cheng, & Melekian, 2018), with special attention to interconnection networks. We remark that if F is an optimal strong matching preclusion set, then we may assume that no edge in F is incident with a vertex in F. It follows from the definitions of mp(G) and smp(G) that smp(G) ≤ mp(G) ≤ δ(G).…”

Section: (Strong) Matching Preclusionmentioning

confidence: 99%

Fractional Strong Matching Preclusion of Split-Star Networks

Han¹,

Xiao²,

Ye³

et al. 2019

JMR

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The matching preclusion number of graph G is the minimum size of edges whose deletion leaves the resulting graph without a perfect matching or an almost perfect matching. Let F be an edge subset and F′ be a subset of edges and vertices of a graph G. If G − F and G − F′ have no fractional matching preclusion, then F is a fractional matching preclusion (FMP) set, and F ′is a fractional strong matching preclusion (FSMP) set of G. The FMP (FSMP) number of G is the minimum number of FMP (FSMP) set of G. In this paper, we study fractional matching preclusion number and fractional strong matching preclusion number of split-star networks. Moreover, We categorize all the optimal fractional strong matching preclusion sets of split-star networks.

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Section: (Strong) Matching Preclusionmentioning

confidence: 99%

Fractional Strong Matching Preclusion of Split-Star Networks

Han¹,

Xiao²,

Ye³

et al. 2019

JMR

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“…A set F of edges and vertices is called a strong matching preclusion set (SMP set for short) if G−F has neither a perfect matching nor an almost-perfect matching. The concept of strong matching preclusion was introduced in [14], for more details see [11]. The strong matching preclusion number of a graph G, denoted by smp(G), is given by smp(G) = min{|F | : F is a SMP set}.…”

Section: Matching Preclusion and Its Generalizationsmentioning

confidence: 99%

Fractional strong matching preclusion for two variants of hypercubes

et al. 2019

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Let F be a subset of edges and vertices of a graph G. If G − F has no fractional perfect matching, then F is a fractional strong matching preclusion set of G. The fractional strong matching preclusion number is the cardinality of a minimum fractional strong matching preclusion set. In this paper, we mainly study the fractional strong matching preclusion problem for two variants of hypercubes, the multiply twisted cube and the locally twisted cube, which are two of the most popular interconnection networks. In addition, we classify all the optimal fractional strong matching preclusion set of each.

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“…It also has connections to a number of other theoretical topics, including conditional connectivity and extremal graph theory. We refer the readers to Cheng and Lipták (2007); Cheng et al (2009); Jwo et al (1993); Li et al (2016); Mao et al (2018); Wang et al (2019) for further details and additional references.…”

Section: (Strong) Matching Preclusion Numbermentioning

confidence: 99%

Fractional matching preclusion for generalized augmented cubes

Ma,

Mao,

Cheng

et al. 2019

Preprint

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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. As a generalization, Liu and Liu (2017) recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number of G is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The fractional strong matching preclusion number of G is the minimum number of vertices and edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we obtain the fractional matching preclusion number and the fractional strong matching preclusion number for generalized augmented cubes. In addition, all the optimal fractional strong matching preclusion sets of these graphs are categorized.

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Strong matching preclusion number of graphs

Cited by 23 publications

References 21 publications

Fractional Strong Matching Preclusion of Split-Star Networks

Fractional Strong Matching Preclusion of Split-Star Networks

Fractional strong matching preclusion for two variants of hypercubes

Fractional matching preclusion for generalized augmented cubes

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