Let G = (V,E) be an undirected graph without loops and multiple edges [1], V (G) and E(G) be the sets of vertices and edges of G, respectively. The degree of a vertex x ∈ V (G) is denoted by dG(x), the maximum degree of a vertex of G-by ∆(G), and the chromatic index [2] of G-by χ(G). A graph is regular, if all its vertices have the same degree. If α is a proper edge colouring of the graph G [3]...

In this project, investigation of stress concentration factor is carried out. Some specimens with edge notches, multiple edge notches, and holes are fabricated. While two specimens are hand sawed to produce edge cracks. The stress concentration factor (K) value is compared between the theoretical values found in standard K value chart with our experimental results. Effect of multiple notches is...

Let G be a 4-connected graph. For an edge e of G, we do the following operations on G: first, delete the edge e from G, resulting the graph G − e; second, for all the vertices x of degree 3 in G− e, delete x from G− e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G a e. If G a...

For integers a and b such that 0 ≤ a ≤ b, a graph G is called an [a, b]−graph if a ≤ dG(x) ≤ b for every vertex x of G and a factor F of a graph is called an [a, b]−factor if a ≤ dF (x) ≤ b for every vertex x of F . We prove the following theorems. Let 0 ≤ l ≤ k ≤ r, 0 ≤ s, 0 ≤ u and 1 ≤ t. Then an [r, r+s]−graph has a [k, k+ t]-factor if ks ≤ rt. Moreover, if (k− l)s+ (r−k)u ≤ (r−1)t, then an ...

background and aims. occlusal rims are used to determine the jaw relationships in the transverse and vertical dimensions and estimate the inter-occlusal distance in edentulous patients. it is important to find ways to determine the height and shape of the occlusal rims correctly. the aim of the present study was to determine the exact distance between the oral cavity floor and the incisal edges...

Seiberg–Witten theory is used to obtain new obstructions to the existence of Einstein metrics on 4-manifolds with conical singularities along an embedded surface. In the present article, the cone angle is required to be of the form 2π/p, p a positive integer, but we conjecture that similar results will also hold in greater generality. Recent work on Kähler–Einstein metrics by Chen, Donaldson, S...

1 ACTIVE CONTOURS WITHOUT EDGES Chan and Vese [1] proposed an approximation for the MS segmentation model by following the level-set based curve evolution formulation [2, 3]. Level sets provide an implicit contour representation where an evolving curve is represented with the zerolevel line of a level set function (Figure 1). The basic aim of Chan and Vese (CV) model is to partition a given ima...

In this paper we study the problem of flipping edges in triangulations of polygons and point sets. We prove that if a polygon Qn has k reflex vertices, then any triangulation of Qn can be transformed to another triangulation of Qn with at most O(n + k 2 ) flips. We produce examples of polygons with two triangulations T and T such that to transform T to T requires O(n ) flips. These results are ...

In this paper, we introduce the problem of drawing with “fat” edges. Traditionally, graph drawing algorithms represent vertices as circles and edges as closed curves connecting the vertices. In this paper we consider the problem of drawing graphs with edges of variable thickness. The thickness of an edge is often used as a visualization cue, to indicate importance, or to convey some additional ...