Background: Pre-eclampsia is the most common critical condition during pregnancy. Plasma concentrations of tumor necrosis factor-alpha (TNF-α) and interleukin-1-beta (IL-1β) increase in pregnant women with pre-eclampsia, compared to normal pregnant women. Objective: To investigate the polymorphisms of IL-1β (C+3954T), TNF-α (G- 308A), and (G-238A) in preeclemptic women northeastern Iran. Me...

Let G be a graph with adjacency matrix A(G) and let D(G) the diagonal of degrees G. For every real α ∈ [0, 1], Nikiforov [21] Wang et al. [26] defined matrices Aα(G) Lα(G), respectively, as = αD(G)+(1−α)A(G) Lα(G) αD(G)+(α − 1)A(G). In this paper, we obtain some relationships between eigenvalues these for families graphs, part Aα Lα-spectrum spider display Lα-characteristic polynomials when the...

Let g(n) be the number of ordered factorizations n into numbers larger than 1. We find precise bounds on positive moments g. use these results to estimate n≤x satisfying g(n)≥x α for all α. In addition, let G(n) and g

Background The pro-inflammatory cytokine, tumor necrosis factor-alpha (TNF-α), is a pathogenic element for a number of disorders. Previous studies have reported that the -1031 T/C and -238 G/A polymorphisms in the promoter region of the TNF-α gene are important factors in reproductive-related disorders. One of the most common gynecological diseases of women during the reproductive years is endo...

In this paper we introduce the concept of α-commutator which its definition is based on generalized conjugate classes. With this notion, α-nilpotent groups, α-solvable groups, nilpotency and solvability of groups related to the automorphism are defined. N(G) and S(G) are the set of all nilpotency classes and the set of all solvability classes for the group G with respect to different automorphi...

Let G be a connected graph, suppose that v is a vertex of G, and denote the subgraph formed from G by deleting vertex v by G \ v. Denote the algebraic connectivities of G and G \ v by α(G) and α(G \ v), respectively. In this paper, we consider the functions φ(v) = α(G) − α(G \ v) and κ(v) = α(G\v) α(G) , provide attainable upper and lower bounds on both functions, and characterise the equality ...

The stability number of a graph G, denoted by α(G), is the cardinality of a maximum stable set, and μ(G) is the cardinality of a maximum matching in G. If α(G) + μ(G) equals its order, then G is a König-Egerváry graph. We call G an α-square-stable graph if α(G) = α(G), where G denotes the second power of G. These graphs were first investigated by Randerath and Wolkmann, [18]. In this paper we o...

The analogue of Hadwiger’s conjecture for the immersion order states that every graph G contains Kχ(G) as an immersion. If true, this would imply with n vertices and independence number α K⌈nα⌉ best currently known bound is due to Gauthier, Le Wollan, who recently proved a clique on ⌈χ(G)−43.54⌉ vertices. Their result implies n-vertex ⌈n3.54α−1.13⌉ We improve all α≥3, by showing α≥3 ⌊n2.25α−f(α...

Let G be a graph of order n with clique number ω(G), chromatic number χ(G) and independence number α(G). We show that χ(G) ≤ n+ω+1−α 2 . Moreover, χ(G) ≤ n+ω−α 2 , if either ω + α = n + 1 and G is not a split graph or α+ω = n−1 and G contains no induced Kω+3−C5.