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...

This study investigated the change in interproximal force (IPF) in mandibular anterior teeth during retention and the relationship between the irregularity index before orthodontic treatment and the IPF. The effect that an erupting third molar had on IPF was also examined. Forty treated patients (40 with extraction of four bicuspids) were followed for 18 months during the retention phase. The i...

An edge irregular total k-labeling φ : V ∪ E → {1, 2, . . . , k} of a graph G = (V,E) is a labeling of vertices and edges of G in such a way that for any different edges uv and u′v′ their weights φ(u) +φ(uv) +φ(v) and φ(u′) +φ(u′v′) +φ(v′) are distinct. The total edge irregularity strength, tes(G), is defined as the minimum k for which G has an edge irregular total k-labeling. In this paper, we...

A total vertex irregular k-labeling φ of a graph G is a labeling of the vertices and edges of G with labels from the set {1, 2, . . . , k} in such a way that for any two different vertices x and y their weights wt(x) and wt(y) are distinct. Here, the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x. The minimum k for which the graph G...

For a simple graph G = (V,E) with the vertex set V and the edge set E , a vertex irregular total k -labeling f : V ∪E → {1, 2, . . . , k} is a labeling ∗ Also at Department of Mathematics, Faculty of Mathematics and Sciences, University of Gadjah Mada, Yogyakarta, Indonesia. D. INDRIATI ET AL. /AUSTRALAS. J. COMBIN. 65 (1) (2016), 14–26 15 of vertices and edges of G in such a way that for any t...

<p>Foster (1932) performed a mathematical census for all connected symmetric cubic (trivalent) graphs of order <em>n</em> with <em>n </em>≤ 512. This then was continued by Conder et al. (2006) and they obtained the complete list ≤ 768. In this paper, we determine total vertex irregularity strength such Foster. As result, values strengths from Foster strengthen conj...

It is easily observed that the vertices of a simple graph cannot have pairwise distinct degrees. This means no order at least two is, in this way, irregular. However, multigraph can be Chartrand et al., 1988, posed following problem: loopless multigraph, how one determine fewest parallel edges required to ensure all degrees? problem known as labeling and, for its solution, al. introduced irregu...