‎Let $G$ be a finite group which is not a cyclic $p$-group‎, ‎$p$ a prime number‎. ‎We define an undirected simple graph $Delta(G)$ whose‎ ‎vertices are the proper subgroups of $G$, which are not contained in the‎ ‎Frattini subgroup of $G$ and two vertices $H$ and $K$ are joined by an edge‎ ‎if and only if $G=langle H‎ , ‎Krangle$‎. ‎In this paper we classify finite groups with planar graph‎. ‎...

Neural tube closure is a critical developmental event that relies on actomyosin contractility to facilitate specific processes such as apical constriction, tissue bending, and directional cell rearrangements. These complicated processes require the coordinated activities of Rho-Kinase (Rock), to regulate cytoskeletal dynamics and actomyosin contractility, and the Planar Cell Polarity (PCP) path...

The covering graph of a lattice which is contained in an ordered set with a planar covering graph is itself planar. AMS subject classifications (1980). 06A10

background: acute renal failure describes as a syndrome by rapid decline in the ability of the kidney to eliminate waste products, regulate acid–base balance, and manage water homeostasis. when this impairment is prolonged and entered chronic phase, erythropoietin secretion by this organ is decreasing and toxic metabolic accumulates and causes hematological changes include decrease of hct, mcv ...

Objective(s): We recently developed a new uptake index method for 123I-metaiodobenzylguanidine (123I-MIBG) heart uptake measurements by using planar images (radioisotope angiography and planar image) for the diagnosis of Lewy body disease (LBD), including Parkinson’s disease (PD) and dementia with Lewy bodies(DLB). However, the diagnostic accuracy of the uptake index was approximately equal to ...

The core planar polarity pathway coordinates epithelial cell polarity during animal development, and loss of its activity gives rise to a range of defects, from aberrant morphogenetic cell movements to failure to correctly orient structures, such as hairs and cilia. The core pathway functions via a mechanism involving segregation of its protein components to opposite cells ends, where they form...

In 1988, Seiya Negami published a conjecture stating that a graph G has a finite planar cover (i.e. a homomorphism from some planar graph onto G which maps the vertex neighbourhoods bijectively) if and only if G embeds in the projective plane. Though the ”if” direction is easy, and over ten related research papers have been published during the past 20 years of investigation, this beautiful con...

A graph G has a planar cover if there exists a planar graph H , and a homomorphism φ : H → G that maps the neighbours of each vertex bijectively. Each graph that has an embedding in the projective plane also has a finite planar cover. Negami conjectured the converse in 1988. This conjecture holds as long as no minor-minimal non-projective graph has a finite planar cover. From the list there rem...