In a visual cryptography scheme, a secret image is encoded into n shares, in the form of transparencies. The shares are then distributed to n participants. Qualified subsets of participants can recover the secret image by superimposing their transparencies, but non-qualified subsets of participants have no information about the secret image. Pixel expansion, which represents the number of subpi...

An r-matching in a graph G is a collection of edges in G such that the distance between any two edges is at least r. This generalizes both matchings and induced matchings as matchings are 1-matchings and induced matchings are 2-matchings. In this paper, we estimate the minimum and maximum number of r-matchings in a tree with fixed order.

We consider simple undirected graphs. An edge subset A of G is called an induced n{star packing of G if every component of the subgraph G[A] induced by A is a star with at most n edges and is an induced subgraph of G. We consider the problem of nding an induced n{star packing of G that covers the maximum number of vertices. This problem is a natural generalization of the classical matching prob...

A set S  V is a induced -paired dominating set if S is a dominating set of G and the induced subgraph is a perfect matching. The induced paired domination number ip(G) is the minimum cardinality taken over all paired dominating sets in G. The minimum number of colours required to colour all the vertices so that adjacent vertices do not receive the same colour and is denoted by (G). The a...

let $g=(v,e)$ be a‎ ‎simple graph of order $n$ and size $m$‎. ‎an $r$-matching of $g$ is ‎a set of $r$ edges of $g$ which no two of them have common vertex‎. ‎the hosoya index $z(g)$ of a graph $g$ is defined as the total‎ ‎number of its matchings‎. ‎an independent set of $g$ is a set of‎ ‎vertices where no two vertices are adjacent‎. ‎the ‎merrifield-simmons index of $g$ is defined as the tota...

An induced matching in a graph is a set of edges whose endpoints induce a 1-regular subgraph. It is known that every n-vertex graph has at most 10 ≈ 1.5849 maximal induced matchings, and this bound is best possible. We prove that every n-vertex triangle-free graph has at most 3 ≈ 1.4423 maximal induced matchings, and this bound is attained by every disjoint union of copies of the complete bipar...

We investigate the origin of the matching effect observed in superconducting Nb films containing regular arrays of holes near the zero-field critical temperature. We find “dips” in the resistance vs magnetic field curves at matching fields where the magnitude of the magnetic flux threading each unit cell is an integer number of the flux quantum. By comparing the magnetic field dependences of th...

The concept of embedded matching in a weighted graph is introduced, and the maximum cardinality of an embedded matching is computed. On the other hand, consider the following problem induced by a short covering. Given a prime power q, the number c(q) denotes the minimum cardinality of a subset H of Fq which satisfies the following property: every element in this space differs in at most 1 coord...

Question and answering service is one of the popular services in the World Wide Web. The main goal of these services is to finding the best answer for user's input question as quick as possible. In order to achieve this aim, most of these use new techniques foe question matching. . We have a lot of question and answering services in Persian web, so it seems that developing a question matching m...

An induced matching in a graph G = (V,E) is a matching M such that (V,M) is an induced subgraph of G. Clearly, among two vertices with the same neighbourhood (called twins) at most one is matched in any induced matching, and if one of them is matched then there is another matching of the same size that matches the other vertex. Motivated by this, Kanj, Pelsmajer, Schaefer and Xia [10] studied i...