Uncertain graphs are employed to describe graph models with indeterministicinformation that produced by human beings. This paper aims to study themaximum matching problem in uncertain graphs.The number of edges of a maximum matching in a graph is called matching numberof the graph. Due to the existence of uncertain edges, the matching number of an uncertain graph is essentially an uncertain var...

language is a system and every system has rules that govern the structure of its vocabulary. the rules of the arabic language are based on the vowels that consistent with the meanings used in the context represent the words' position. there are some basic rules in addition to vowels which are mostly seen in the written texts. one of these rules is the matching rule that refers to the condi...

Let $G=(V,E)$ be a simple connected graph. A matching $M$ in a graph $G$ is a collection of edges of $G$ such that no two edges from $M$ share a vertex. A matching $M$ is maximal if it cannot be extended to a larger matching in $G$. The cardinality of any smallest maximal matching in $G$ is the saturation number of $G$ and is denoted by $s(G)$. In this paper we study the saturation numbe...

Caro, Davila, and Pepper recently proved δ(G)α(G)≤Δ(G)μ(G) for every graph G with minimum degree δ(G), maximum Δ(G), independence number α(G), matching μ(G). Answering some problems they posed, we characterize the extremal graphs δ(G)<Δ(G) as well δ(G)=Δ(G)=3.

we find recursive formulae for the number of perfect matchings in a graph g by splitting g into subgraphs h and q. we use these formulas to count perfect matching of p hypercube qn. we also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in g, is the graph constructed from by deleting edges with an en...

A bipartite graph G = (U, V ;E) is called ǫ-regular if the edge density of every sufficiently large induced subgraph differs from the edge density of G by no more than ǫ. If, in addition, the degree of each vertex in G is between (d− ǫ)n and (d+ ǫ)n, where d is the edge density of G and |U | = |V | = n, then G is called super (d, ǫ)-regular. In [Combinatorica, 19 (1999), pp. 437– 452] it was sh...

The matching preclusion number of a graph is the minimum number of neither edges whose deletion in a graph has a neither perfect matching nor an almost perfect matching. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently the conditional matching preclusion number of a graph was introduced to look for sets beyond those induced by a single...