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...

In this paper, we tighten the concise Turán theorem for irregular graphs, using spectral and non-spectral proofs. We then investigate to what extent Turán’s theorem can be similarly strengthened for generalized r-partite graphs.

one of the important issues in hydraulic engineering is inspection of local scour depth around bridge pier. using piles is one of the ways for confronting local scour and erosion. in this study, the experiments were conducted in an 8m long, 0.5m deep and 0.25m wide flume. and the effectof using piles and number of them observed on the amount of scour in three different frude numbers. the shape ...

Bell's degree-variance Var$!{}_{B}$ for a graph $G$, with the degree sequence ($d_1,d_2,cdots,d_n$) and size $m$, is defined as$Var!_{B} (G)=frac{1}{n} sum _{i=1}^{n}left[d_{i} -frac{2m}{n}right]^{2}$.In this paper, a new version of the irregularity measures of variance-type, denoted by $Var_q$, is introduced and discussed. Based on a comparative study, it is demonstrated that the n...

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...

It has been shown that, from the prevalence point of view, elements of the S spaces are almost surely multifractal, while the Hölder exponent at almost every point is almost surely equal to the maximum Hölder exponent. We show here that typical elements of S are very irregular by proving that they almost surely satisfy a weak irregularity property: there exists a local irregularity exponent whi...