Matching preclusion number in product graphs

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

doi:10.1016/j.tcs.2018.06.050

Cited by 16 publications

(6 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Section 3, we study the above extremal problems on fractional matching preclusion number. The results in this paper can be viewed as the fractional matching preclusion number analogues of those in [32]. So the basic structure of some of the proofs are similar.…”

Section: Extremal Problemmentioning

confidence: 68%

Fractional matching preclusion number of graphs

Zou¹,

Mao²,

Wang³

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

The fractional matching preclusion number of a graph G, denoted by f mp(G), is the minimum number of edges whose deletion results in a graph that has no fractional perfect matchings. In this paper, we first give some sharp upper and lower bounds of fractional matching preclusion number. Next, graphs with large and small fractional matching preclusion number are characterized, respectively. In the end, we investigate some extremal problems on fractional matching preclusion number.

show abstract

Section: Extremal Problemmentioning

confidence: 68%

Fractional matching preclusion number of graphs

Zou¹,

Mao²,

Wang³

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The matching preclusion number of a graph G, denoted by mp(G), is the size of a smallest matching preclusion set of G. Any such optimal set is called an optimal matching preclusion set. The concept of matching preclusion was introduced by Birgham et al (Birgham, Harry, Biolin, & Yellen, 2005) and further studied in (Cheng, Lesniak, Lipman, & Lipták, 2008;Cheng, Lesniak, Lipman, Lipták, 2007;Wang, Mao, Cheng, & Zou, 2019;Wang, Melekian, Cheng, & Mao, 2019), with special attention to interconnection networks. For graphs with an even number of vertices, an obvious matching preclusion set is the set of edges incident with a single vertex; such a set is called a trivial matching preclusion set.…”

Section: (Strong) Matching Preclusionmentioning

confidence: 99%

Fractional Strong Matching Preclusion of Split-Star Networks

Han¹,

Xiao²,

Ye³

et al. 2019

JMR

View full text Add to dashboard Cite

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.

show abstract

“…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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Matching preclusion number in product graphs

Cited by 16 publications

References 22 publications

Fractional matching preclusion number of graphs

Fractional matching preclusion number of graphs

Fractional Strong Matching Preclusion of Split-Star Networks

Fractional matching preclusion for generalized augmented cubes

Contact Info

Product

Resources

About