Fractional matching preclusion for arrangement graphs

Ma, Tianlong; Mao, Yaping; Cheng, Eddie; Wang, Jinling

doi:10.1016/j.dam.2019.07.014

Cited by 15 publications

(3 citation statements)

References 12 publications

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“…For example, the spectra of arrangement graphs were studied in [2,7], the faulty tolerances were investigated in [36,39], and the conditional fault tolerance and the fault diagnosability were given in [40,41]. For more works on the arrangement graphs, we refer the reader to [2,8–12,19,19,23,31,38] and the references therein. These investigations show that this class of graphs admit many nice properties, such as hierarchical structure, simple shortest path routing, high connectivity, and so on.…”

Section: Introductionmentioning

confidence: 99%

The symmetry property of (n,k)‐arrangement graph

Yin

Yan

Zhou

et al. 2021

Journal of Graph Theory

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The ( n , k )‐arrangement graph A ( n , k ) with 1 ≤ k ≤ n − 1, is the graph with vertex set the ordered k‐tuples of distinct elements in { 1 , 2 , … , n } and with two k‐tuples adjacent if they differ in exactly one of their coordinates. The ( n , k )‐arrangement graph was proposed by Day and Tripathi in 1992, and is a widely studied interconnection network topology. The Johnson graph J ( n , k ) with 1 ≤ k ≤ n − 1, is the graph with vertex set the k‐element subsets of { 1 , 2 , … , n }, and with two k‐element subsets adjacent if their intersection has k − 1 elements. In 1989, Brouwer, Cohen and Neumaier determined the automorphism group of J ( n , k ), and in 2015, Dobson and Malnič proved that J ( n , k ) a is Cayley graph if and only if ( n , k ) = ( 8 , 3 ), ( 32 , 3 ) or ( n , 2 ) with n ≡ 3 ( sans-serifmod 4 ) being a prime‐power. In this article we prove that sans-serifAut ( A ( n , k ) ) ≅ S n × S k, and as a byproduct, A ( n , k ) is a normal cover of J ( n , k ). Furthermore, A ( n , k ) is a Cayley graph if and only if ( n , k ) = ( 33 , 4 ), ( 11 , 4 ), ( 9 , 4 ), ( 12 , 5 ), ( 8 , 5 ), ( 9 , 6 ), ( 32 , 29 ), ( 33 , 30 ), ( n , 1 ), ( n , n − 1 ), ( n , n − 2 ), ( q , 2 ) or ( q + 1 , 3 ), where q is a prime‐power. Note that the graph A ( n , n − 1 ) is called the n‐star graph, and its automorphism group can be deduced from a general result given by Feng in 2006. In 1998, Chiang and Chen proved that A ( n , n − 2 ) is a Cayley graph on the alternating group A n, and in 2011, Zhou determined the automorphism group of A ( n , n − 2 ).

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Section: Introductionmentioning

confidence: 99%

The symmetry property of (n,k)‐arrangement graph

Yin

Yan

Zhou

et al. 2021

Journal of Graph Theory

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“…A FMP set of minimum cardinality is called optimal. We refer the readers to [10,12] for more details and additional references. , where is the minimum degree of .…”

Section: Introduction a Matchingmentioning

confidence: 99%

Fractional strong matching preclusion of some Cartesian product graphs

Zhu

Zhang

2021

J. Phys.: Conf. Ser.

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The fractional strong matching preclusion number of a graph is the minimum number of edges and vertices whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we obtain the fractional strong matching preclusion number for the Cartesian product of a graph and a cycle. As an application, the fractional strong matching preclusion number for torus networks is also obtained.

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“…The fractional matching preclusion number (FMP number for short) of G, denoted by f mp(G), is the minimum size of FMP sets of G, that is, f mp(G) = min{|F | : F is an FMP set}. We refer the readers to [10,12] for more details and additional references.…”

Section: Introductionmentioning

confidence: 99%

Fractional strong matching preclusion for Cartesian product graphs

Zhu,

2020

Preprint

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The strong matching preclusion number of a graph, introduced by Park and Ihm in [13], is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, the fractional strong matching preclusion number of a graph is the minimum number of edges and vertices whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we obtain the fractional strong matching preclusion number for Cartesian product graphs.As an application, the fractional strong matching preclusion number for torus networks is obtained.

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Fractional matching preclusion for arrangement graphs

Cited by 15 publications

References 12 publications

The symmetry property of (n,k)‐arrangement graph

The symmetry property of (n,k)‐arrangement graph

Fractional strong matching preclusion of some Cartesian product graphs

Fractional strong matching preclusion for Cartesian product graphs

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