Matching Preclusion Number Of Graph Research Articles

Fractional matching preclusion of product networks

The matching preclusion number of a graph, introduced in [2] as a fault analysis, is the minimum number of edges whose deletion leaves a resulting graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu [14] recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number of graph is the minimum number of edges whose deletion results in a graph that has no fractional perfect matching. If the sets of edges of the graph attaining the minimum are precisely those incident to a single vertex of minimum degree, we say such graph is fractional super matched. In this paper, the upper and lower bounds for the fractional matching preclusion number for Cartesian product, direct product, strong product, and lexicographic product are obtained, and we give sufficient conditions for such graphs to be fractional super matched.

Fractional matching preclusion number of graphs and the perfect matching polytope

Let G be a graph with an even number of vertices. The matching preclusion number of G, denoted by mp(G), is the minimum number of edges whose deletion leaves the resulting graph without a perfect matching. We introduced a 0–1 linear program which can be used to find the matching preclusion number of graphs. In this paper, by relaxing of the 0–1 linear program we obtain a linear program and call its optimal objective value as fractional matching preclusion number of graph G, denoted by mp f (G). We show mp f (G) can be computed in polynomial time for any graph G. By using the perfect matching polytope, we transform it into a new linear program whose optimal value equals the reciprocal of mp f (G). For bipartite graph G, we obtain an explicit formula for mp f (G) and show that ⌊ mp f (G) ⌋ is the maximum integer k such that G has a k-factor. Moreover, for any two bipartite graphs G and H, we show mp f (Gs H) ⩾ mp f (G) + ⌊ mp f (H) ⌋ , where Gs H is the Cartesian product of G and H. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Fractional Strong Matching Preclusion of Split-Star Networks

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.

Matching Preclusion Number of Radix Triangular Mesh with Odd Vertices

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.