We investigate several related measures of peripherality and centrality for vertices edges in networks, including the Mostar index which was recently introduced as a measure both networks. refute conjecture on maximum possible bipartite graphs. asymptotically answer another problem difference between irregularity trees. also prove number extremal bounds computational complexity results about in...

UNLABELLED The aim of this study was to evaluate quantitatively the heterogeneity of lung perfusion scans in patients with primary pulmonary hypertension (PPH) and to compare it with the severity of disease. METHODS Lung perfusion scans were obtained on 22 patients with PPH and 12 age-matched control subjects. The perfused area rates (PARs) were calculated by dividing the lung area in each 10...

We investigate the irregularity strength (s(G)) and total vertex irregularity strength (tvs(G)) of circulant graphs Cin(1, 2, . . . , k) and prove that tvs(Cin(1, 2, . . . , k)) = ⌈ n+2k 2k+1 ⌉ , while s(Cin(1, 2, . . . , k)) = ⌈ n+2k−1 2k ⌉ except if either n = 2k + 1 or if k is odd and n ≡ 2k + 1(mod4k), then s(Cin(1, 2, . . . , k)) = ⌈ n+2k−1 2k ⌉ + 1.

A labeling of edges and vertices a simple graph \(G(V,E)\) by mapping \(\Lambda :V\left( G \right) \cup E\left( \to \left\{ { 1,2,3, \ldots ,\Psi } \right\}\) provided that any two pair have distinct weights is called an edge irregular total \(\Psi\)-labeling. If \(\Psi\) minimum \(G\) admits -labelling, then the irregularity strength (TEIS) denoted \(\mathrm{tes}\left(G\right).\) In this paper...

OBJECTIVE The aim of this longitudinal study, comprising young adults without orthodontic treatment, was to assess spontaneous changes in lower dental arch alignment and dimensions. METHODS Twenty pairs of dental casts of the lower arch, obtained at different time intervals, were compared. Dental casts obtained at T1 (mean age = 20.25) and T2 (mean age = 31.2) were compared by means of paired...

INTRODUCTION A retainer bonded to the lingual surfaces of the mandibular canines (3-3 retainer) is a widely used type of retention. Our aim in this study was to assess the effectiveness of the 3-3 mandibular lingual stainless steel retainer to prevent relapse of the orthodontic treatment in the mandibular anterior region. METHODS The sample consisted of the dental casts of 235 consecutively t...

Progressive collapse is defined as the spread of an initial damage from one member to another, leading to extensive partial or total collapse of the structure. In this research, the potential of progressive collapse due to a sudden removal of vertical load-bearing elements in reinforced concrete buildings structures with different floor plans such as geometrical regular and irregular floor plan...