For a simple, undirected graph G with, at most one isolated vertex and no edges, labeling f:E(G)→{1,2,…,k1} of positive integers to the edges is called irregular if weights each has different value. The integer k1 then irregularity strength G. If number vertices in or order |G|, μ:E(G)→{1,2,…,k2} modular remainder divided by |G| k2 disjoint union two more graphs, denoted ‘+’, an operation where...

PURPOSE To investigate the changes in irregular and regular corneal astigmatism with age in eyes that underwent cataract surgery (surgery group) and in eyes that did not undergo surgery (nonsurgery group). METHODS We enrolled 120 eyes in each of four age groups in the surgery and nonsurgery groups: (1) 50 to 59 years of age, (2) 60 to 69 years of age, (3) 70 to 79 years of age, and (4) older ...

The study of graphs and networks accomplished by topological measures plays an applicable task to obtain their hidden topologies. This procedure has been greatly used in cheminformatics, bioinformatics, biomedicine, where estimations based on graph invariants have made available for effectively communicating with the different challenging tasks. Irregularity are mostly characterization nonregul...

A closed walk in a connected graph G that contains every edge of G exactly once is an Eulerian circuit. A graph is Eulerian if it contains an Eulerian circuit. It is well known that a connected graph G is Eulerian if and only if every vertex of G is even. An Eulerian walk in a connected graph G is a closed walk that contains every edge of G at least once, while an irregular Eulerian walk in G i...

I construct normal del Pezzo surfaces, and regular weak del Pezzo surfaces as well, with positive irregularity q > 0. Such things can happen only over nonperfect fields. The surfaces in question are twisted forms of nonnormal del Pezzo surfaces, which were classified by Reid. The twisting is with respect to the flat topology and infinitesimal group scheme actions. The twisted surfaces appear as...

congestive heart failure (chf) remains to be one of the major cardiovascular disorders in the world. due to the prevalence of chf related issues, it is prudent to seek out new prognostic predictors that would facilitate the prevention, monitoring, and treatment of the disease on a daily basis. a detection approach using entropy measures extracted from surface electrocardiograms (ecgs) and class...

High irregularity of Iris tissue is the main reason of its usage in identification systems. In some literatures, this irregularity has been known as a result of a stochastic genetic process. In this paper an efficient method based on the Poincaré section and modified version of fractal dimension is used. In fact, this method is introduced a pattern for decision making about series specification...

Let G be a simple graph with no isolated edges and at most one isolated vertex. For a positive integer w, a w-weighting of G is a map f : E(G) → {1, 2, . . . , w}. An irregularity strength of G, s(G), is the smallest w such that there is a w-weighting of G for which ∑

Irregularities in force output are present throughout human movement and can impair task performance. We investigated the presence of a large force discontinuity (after-peak reduction, APR) that appeared immediately following peak in maximal effort ramp contractions performed with the thumb adductor and ankle dorsiflexor muscles in 25 young adult participants (76% males, 24% females; M age 24.4...

Consider a simple graph G with no isolated edges and at most one isolated vertex. A labeling w : E(G) → {1, 2, . . . ,m} is called product-irregular, if all product degrees pdG(v) = ∏ e3v w(e) are distinct. The goal is to obtain a product-irregular labeling that minimizes the maximum label. This minimum value is called the product irregularity strength. The analogous concept of irregularity str...