Fractional matching preclusion for radix triangular mesh

2019 ◽  
Vol 11 (04) ◽  
pp. 1950048
Author(s):  
Xia Wang ◽  
Tianlong Ma ◽  
Jun Yin ◽  
Chengfu Ye
Keyword(s):  
Perfect Matching ◽  
Triangular Mesh ◽  
Perfect Matchings ◽  
Minimum Number ◽  
Fractional Perfect Matching

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 recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number (FMP number) of [Formula: see text], denoted by [Formula: see text], is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The fractional strong matching preclusion number (FSMP number) of [Formula: see text], denoted by [Formula: see text], is the minimum number of vertices and edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we study the fractional matching preclusion number and the fractional strong matching preclusion number for the radix triangular mesh [Formula: see text], and all the optimal fractional matching preclusion sets and fractional strong matching preclusion sets of these graphs are categorized.

Fractional Matching Preclusion for (n, k)-Star Graphs

2018 ◽  
Vol 28 (04) ◽  
pp. 1850017 ◽  
Author(s):  
Tianlong Ma ◽  
Yaping Mao ◽  
Eddie Cheng ◽  
Jinling Wang
Keyword(s):  
Perfect Matching ◽  
Perfect Matchings ◽  
Star Graphs ◽  
Minimum Number ◽  
Fractional Perfect Matching

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 introduced the concept of fractional matching preclusion number in 2017. The Fractional Matching Preclusion Number (FMP 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 (FSMP number) of G is the minimum number of vertices and/or edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we obtain the FMP number and the FSMP number for (n, k)-star graphs. In addition, all the optimal fractional strong matching preclusion sets of these graphs are categorized.

scholarly journals Fractional Matching Preclusion for Restricted Hypercube-Like Graphs

2019 ◽  
Vol 19 (03) ◽  
pp. 1940010
Author(s):  
HUAZHONG LÜ ◽  
TINGZENG WU
Keyword(s):  
Interconnection Networks ◽  
Perfect Matching ◽  
Parallel Systems ◽  
Perfect Matchings ◽  
Minimum Number ◽  
Fractional Perfect Matching

The restricted hypercube-like graphs, variants of the hypercube, were proposed as desired interconnection networks of parallel systems. The matching preclusion number of a graph is the minimum number of edges whose deletion results in the graph with neither perfect matchings nor almost perfect matchings. The fractional perfect matching preclusion and fractional strong perfect matching preclusion are generalizations of the matching preclusion. In this paper, we obtain fractional matching preclusion number and fractional strong matching preclusion number of restricted hypercube-like graphs, which extend some known results.

Matching Preclusion Number of Radix Triangular Mesh with Odd Vertices

2018 ◽  
Vol 18 (02n03) ◽  
pp. 1850010
Author(s):  
CHUNXIA WANG ◽  
YALAN LI ◽  
SHUMIN ZHANG ◽  
CHENGFU YE ◽  
XIA WANG
Keyword(s):  
Perfect Matching ◽  
Triangular Mesh ◽  
Minimum Number

The matching preclusion number of graph G is the minimum number of edges whose deletion leaves the resulting graph without a perfect matching or almost-perfect matching. The strong matching preclusion number of a graph G is the minimum number of vertices and edges whose deletion leaves the resulting graph without a perfect matching or an almost-perfect matching. The conditional matching preclusion number of G is the minimum number of edges whose deletion leaves the resulting graph with no isolated vertices and without a perfect matching or almost-perfect matching. In this paper, we study the matching preclusion number of radix triangular mesh with an odd number of vertices, and strong matching preclusion number and conditional matching preclusion number of radix triangular mesh. Also, we obtained the radix triangular mesh with an even number of vertices is super strongly matched and conditionally super matched.

scholarly journals Fractional strong matching preclusion of some Cartesian product graphs

2021 ◽  
Vol 2132 (1) ◽  
pp. 012033
Author(s):  
Bo Zhu ◽  
Shumin Zhang ◽  
Chenfu Ye
Keyword(s):  
Perfect Matching ◽  
Cartesian Product ◽  
Product Graphs ◽  
Minimum Number ◽  
Cartesian Product Graphs ◽  
Torus Networks ◽  
Fractional Perfect Matching

Abstract 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.

scholarly journals On the Number of Perfect Matchings in Random Lifts

2010 ◽  
Vol 19 (5-6) ◽  
pp. 791-817 ◽  
Author(s):  
CATHERINE GREENHILL ◽  
SVANTE JANSON ◽  
ANDRZEJ RUCIŃSKI
Keyword(s):  
Asymptotic Formula ◽  
Complete Graph ◽  
Pairwise Disjoint ◽  
Perfect Matching ◽  
Perfect Matchings ◽  
Lattice Points ◽  
Laplace’S Method ◽  
Second Moment ◽  
Multiple Dimensions ◽  
Laplace's Method

Let G be a fixed connected multigraph with no loops. A random n-lift of G is obtained by replacing each vertex of G by a set of n vertices (where these sets are pairwise disjoint) and replacing each edge by a randomly chosen perfect matching between the n-sets corresponding to the endpoints of the edge. Let XG be the number of perfect matchings in a random lift of G. We study the distribution of XG in the limit as n tends to infinity, using the small subgraph conditioning method.We present several results including an asymptotic formula for the expectation of XG when G is d-regular, d ≥ 3. The interaction of perfect matchings with short cycles in random lifts of regular multigraphs is also analysed. Partial calculations are performed for the second moment of XG, with full details given for two example multigraphs, including the complete graph K4.To assist in our calculations we provide a theorem for estimating a summation over multiple dimensions using Laplace's method. This result is phrased as a summation over lattice points, and may prove useful in future applications.

scholarly journals Face-Width of Pfaffian Braces and Polyhex Graphs on Surfaces

10.37236/3540 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Dong Ye ◽  
Heping Zhang
Keyword(s):  
Bipartite Graph ◽  
Polynomial Time ◽  
Perfect Matching ◽  
Cartesian Product ◽  
Perfect Matchings ◽  
Face Width ◽  
Graphs On Surfaces ◽  
Positive Genus ◽  
Pfaffian Graph

A graph $G$ with a perfect matching is Pfaffian if it admits an orientation $D$ such that every central cycle $C$ (i.e. $C$ is of even size and $G-V(C)$ has a perfect matching) has an odd number of edges oriented in either direction of the cycle. It is known that the number of perfect matchings of a Pfaffian graph can be computed in polynomial time. In this paper, we show that every embedding of a Pfaffian brace (i.e. 2-extendable bipartite graph)  on a surface with a positive genus has face-width at most 3.  Further, we study Pfaffian cubic braces and obtain a characterization of Pfaffian polyhex graphs: a polyhex graph is Pfaffian if and only if it is either non-bipartite or isomorphic to the cube, or the Heawood graph, or the Cartesian product $C_k\times K_2$ for even integers $k\ge 6$.

Fractional Strong Matching Preclusion for DHcube

2021 ◽  
Vol 31 (01) ◽  
pp. 2150001
Author(s):  
He Zhang ◽  
Jinyu Zou ◽  
Shuangshuang Zhang ◽  
Chengfu Ye
Keyword(s):  
Perfect Matching ◽  
Minimum Size ◽  
Fractional Perfect Matching

Let [Formula: see text] be a set edges and [Formula: see text] be a set of edges and/or vertices of a graph [Formula: see text], then [Formula: see text] (resp. [Formula: see text]) is a fractional matching preclusion set (resp. fractional strong matching preclusion set) if [Formula: see text] (resp. [Formula: see text]) contains no fractional perfect matching. The fractional matching preclusion number (resp. fractional strong matching preclusion number) of [Formula: see text] is the minimum size of fractional matching preclusion set (resp. fractional strong matching preclusion set) of [Formula: see text]. In this paper, we obtain the fractional matching preclusion number and fractional strong matching preclusion number of the DHcube [Formula: see text] for [Formula: see text]. In addition, all the optimal fractional matching preclusion sets and fractional strong matching preclusion sets of these graphs are categorized.

scholarly journals Commuting decomposition of Kn1,n2,...,nk through realization of the product A(G)A(GPk )

2018 ◽  
Vol 6 (1) ◽  
pp. 343-356
Author(s):  
K. Arathi Bhat ◽  
G. Sudhakara
Keyword(s):  
Chromatic Number ◽  
Perfect Matching ◽  
Domination Number ◽  
Perfect Matchings ◽  
Factor Graph ◽  
Vertex Set ◽  
Graph Parameters

Abstract In this paper, we introduce the notion of perfect matching property for a k-partition of vertex set of given graph. We consider nontrivial graphs G and GPk , the k-complement of graph G with respect to a kpartition of V(G), to prove that A(G)A(GPk ) is realizable as a graph if and only if P satis_es perfect matching property. For A(G)A(GPk ) = A(Γ) for some graph Γ, we obtain graph parameters such as chromatic number, domination number etc., for those graphs and characterization of P is given for which GPk and Γ are isomorphic. Given a 1-factor graph G with 2n vertices, we propose a partition P for which GPk is a graph of rank r and A(G)A(GPk ) is graphical, where n ≤ r ≤ 2n. Motivated by the result of characterizing decomposable Kn,n into commuting perfect matchings [2], we characterize complete k-partite graph Kn1,n2,...,nk which has a commuting decomposition into a perfect matching and its k-complement.

scholarly journals On the König deficiency of zero-reducible graphs

2019 ◽  
Vol 39 (1) ◽  
pp. 273-292
Author(s):  
Miklós Bartha ◽  
Miklós Krész
Keyword(s):  
Perfect Matching ◽  
Linear Time ◽  
Perfect Matchings ◽  
Covering Number ◽  
Matching Number ◽  
Empty Graph ◽  
Reduction System ◽  
Vertex Covering ◽  
Np Complete ◽  
The Difference

Abstract A confluent and terminating reduction system is introduced for graphs, which preserves the number of their perfect matchings. A union-find algorithm is presented to carry out reduction in almost linear time. The König property is investigated in the context of reduction by introducing the König deficiency of a graph G as the difference between the vertex covering number and the matching number of G. It is shown that the problem of finding the König deficiency of a graph is NP-complete even if we know that the graph reduces to the empty graph. Finally, the König deficiency of graphs G having a vertex v such that $$G-v$$G-v has a unique perfect matching is studied in connection with reduction.

A Short Note of Strong Matching Preclusion for a Class of Arrangement Graphs

2020 ◽  
Vol 30 (01) ◽  
pp. 2050001
Author(s):  
Shuangshuang Zhang ◽  
Yuzhi Xiao ◽  
Xia Liu ◽  
Jun Yin
Keyword(s):  
Short Note ◽  
Perfect Matchings ◽  
Minimum Number ◽  
Edge Failure

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. The strong matching preclusion is a well-studied measure for the network invulnerability in the event of edge failure. In this paper, we obtain the strong matching preclusion number for a class of arrangement graphs and categorize their the strong matching preclusion set, which are a supplement of known results.

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