The irregularity strength of a simple graph is the smallest integer k for which there exists a weighting of the edges with positive integers at most k such that all the weighted degrees of the vertices are distinct. In this paper we study the irregularity strength of circulant graphs of degree 4. We find the exact value of the strength for a large family of circulant graphs. © 2005 Elsevier B.V...

In his paper Linear equations in non-commutative fields (Ann. of Math. vol. 32 (1931) pp. 463-477) Professor Oystein Ore defines regularity and irregularity of rings and an "order of irregularity" in such a way that regularity becomes irregularity of order 1. Herewith the following problem is proposed: Do irregular rings of order n>\ really exist? If so of what type are they? In this note these...

This paper proposes a nonparametric steganalysis method for quantization index modulation (QIM) based steganography. The proposed steganalysis method uses irregularity (or randomness) in the test-image to distinguish between the coverand the stego-image. We have shown that plain-quantization (quantization without message embedding) induces regularity in the resulting quantized-image; whereas me...

The total irregularity of a graph G is defined as irrt .G/ D 1 2 P u;v2V.G/ jdG.u/ dG.v/j, where dG.u/ denotes the degree of a vertex u 2 V.G/. In this paper we give (sharp) upper bounds on the total irregularity of graphs under several graph operations including join, lexicographic product, Cartesian product, strong product, direct product, corona product, disjunction and symmetric difference....

in this research, the effect of temperature on the physical and chemical behavior of nylon 66 tire cords in the range of 50-200°c and 16 h testing was studied. the results showed that heat treatment considerably reduced the breaking strength of cords. the intensity of reduction of breaking strength below 100°c and above 120°c was more pronounced than intermediate temperatures. the changes in pr...

AIMS To quantitatively evaluate the changes in corneal irregular astigmatism after laser in situ keratomileusis (LASIK) in relation to the amount of laser ablation. METHODS In 189 eyes of 116 patients undergoing LASIK for myopia, corneal topography was obtained before and 1 month after surgery. Using Fourier harmonic analysis of the topography data, corneal irregular astigmatism (asymmetry an...

Implantable devices capable of several modes of therapy will require differentiation of various ventricular tachyarrhythmias. Three methods of arrhythmia analysis, magnitude-squared coherence, ventricular rate, and irregularity of cycle length were performed for 45 episodes of induced ventricular tachyarrhythmia in 15 patients. Differentiation of monomorphic ventricular tachycardia from polymor...

Let Γ(G) be a set of all simple graphs of order n and sizem, without isolated vertices, with vertex degree sequence d1 ≥ d2 ≥ ·· · ≥ dn > 0. A graph G is regular if and only if d1 = d2 = · · ·= dn. Each mapping Irr : Γ(G) 7→ [0,+∞) with the property Irr(G) = 0 if and only if G is regular, is referred to as irregularity measure of graph. In this paper we introduce some new irregularity measures ...

We make a preliminary investigation into twisted $A_{2n}$ theories of class S. Contrary to common piece folklore, we establish that this type realise variety models Argyres-Douglas while utilising only regular punctures. present an in-depth analysis all $A_2$ trinion theories, analyse their interrelations via partial Higgsing, and discuss some generalised S-dualities.