Albertson [3] has defined the irregularity of a simple undirected graph G = (V,E) as irr(G) = ∑ uv∈E |dG(u)− dG(v)| , where dG(u) denotes the degree of a vertex u ∈ V . Recently, this graph invariant gained interest in the chemical graph theory, where it occured in some bounds on the first and the second Zagreb index, and was named the third Zagreb index [13]. For general graphs with n vertices...

Railway track irregularity surveying is important for the construction and the maintenance of railway lines. With the development of inertial devices, systems based on Inertial Navigation System (INS) have become feasible and popular approaches in track surveying applications. In order to overcome the requirement of high precision control points, this paper proposes a railway track irregularity...

A face irregular entire k-labeling φ : V ∪E ∪F → {1,2, . . . ,k} of a 2-connected plane graph G = (V,E,F) is a labeling of vertices, edges and faces of G in such a way that for any two different faces f and g their weights wφ ( f ) and wφ (g) are distinct. The weight of a face f under a k-labeling φ is the sum of labels carried by that face and all the edges and vertices incident with the face....

The irregularity of a graph G is defined as the sum of weights |d(u) − d(v)| of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. In this paper, some structural properties on trees with maximum (or minimum) irregularity among trees with given degree sequence and trees with given branching number are explored, respectively. Moreover, the correspon...

The propagation of shear waves in an anisotropic fluid saturated porous layer over a prestressed semi-infinite homogeneous elastic half-space lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary has been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for shear waves is derived by using the pertur...

Introduction. The treatment of edentulous patients is always a challenge for the prosthodontists. It is connected with a lot of procedures aiming to reconstruct and replace the lost natural dentition and associated structures of the mandible and maxilla for patients who have lost all their remaining teeth. The basic objectives of complete denture Prosthodontics are the restoration of function, ...

[1] Based on the analysis of a low-order tropical atmosphere-ocean model we propose a nonlinear mechanism explaining several features of the observed El Niño-Southern Oscillation (ENSO) phenomenon: ENSO irregularity, ENSO Amplitude Modulations and decadal tropical climate variability. The mechanism suggested here is based on the idea of homoclinic/heteroclinic orbits, an inherently nonlinear co...

PURPOSE The aim of this study was to identify the relationship between awareness of nutrition labeling and menstrual cycle irregularity in women from a nationally representative sample of the Korean population. METHODS A cross-sectional analysis was performed using hierarchical multivariable logistic regression analysis models. A total of 4,324 women aged 19~54 years from the 2010~2012 Korean...

OBJECTIVE To evaluate the importance of microcalcifications in the detection of breast carcinoma in conventional mammography. METHODS This prospective study was carried out at Aga Khan University Hospital (AKUH). Mammograms of 68 patients with microcalcifications were evaluated. Craniocaudal and oblique views of both breasts were acquired on routine basis with cone compression and magnified v...