There is a model-completion Tn of the theory of a (reflexive) ncoloured graph 〈X,R1, . . . , Rn〉 such that Rn is total, and Ri ◦Rj ⊆ Ri+j for all i, j. For n > 2, the theory Tn is not simple, and does not have the strict order property. The theories Tn combine to yield a non-simple theory T∞ without the strict order property, which does not eliminate hyperimaginaries.

The Graph Minors Theory, developed by Robertson and Seymour, has been one of the most influential mathematical theories in parameterized algorithm design. We present some of the basic algorithmic techniques and methods that emerged from this theory. We discuss its direct meta-algorithmic consequences, we present the algorithmic applications of core theorems such as the grid-exclusion theorem, a...

The purpose of this paper is the study of Cayley graph associated to a semihypergroup(or hypergroup). In this regards first  we associate a Cayley graph to every semihypergroup and then we study theproperties of this graph, such as  Hamiltonian cycles in this  graph.  Also, by some of examples we will illustrate  the properties and behavior of  these Cayley  graphs, in particulars we show that ...

In many real world problems, data sometimes comes from n agents (n≥2), multipolar information exists. For issues that are associated with uncertainty, this information can not be showed with the values of crisp, fuzzy, intuitionistic or bipolar. Graph is one of the mathematical models widely used in different sciences. Ambiguity in a graph where data depends on the n parameter can not be showed...

We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of random noise. Our procedure substantially differs from wavelets-based algorithms. The algorithm has linear complexity and exponential accuracy and is approp...

Bidirectional transformations are useful to maintain consistency between source data and target data. So far, researchers have proposed several theories and tools for bidirectional transformations on tree structures. However, as far as we know, there is no widely-recognized theory for bidirectional transformations on graphs. In this paper, we propose an approach to constructing bidirectional gr...

For any realistic theory of quintessence that allows for a violation of the equivalence principle (VEP), we study the experimental constraints on such theories coming from ordinary matter as well as neutrinos. We discuss and compare constraints from two basically different (extra) contributions to differences of fermion masses: one is due to the vacuum expectation value (vev) of quintessence, a...

for a simple connected graph $g$ with $n$-vertices having laplacian eigenvalues‎ ‎$mu_1$‎, ‎$mu_2$‎, ‎$dots$‎, ‎$mu_{n-1}$‎, ‎$mu_n=0$‎, ‎and signless laplacian eigenvalues $q_1‎, ‎q_2,dots‎, ‎q_n$‎, ‎the laplacian-energy-like invariant($lel$) and the incidence energy ($ie$) of a graph $g$ are respectively defined as $lel(g)=sum_{i=1}^{n-1}sqrt{mu_i}$ and $ie(g)=sum_{i=1}^{n}sqrt{q_i}$‎. ‎in th...

the degree set of a graph is the set of its degrees. kapoor et al. [degree sets for graphs, fund. math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. furthermore, the minimum order of such a graph is determined. a graph is 2-self- centered if its radius and diameter are two. in this paper for ...