We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that arise as lifts of dipoles with voltage assignments in Abelian groups. Further, we construct a family of Cayley graphs of degree d = 3m− 1 and diameter k ≥ 3 of order kmk. By comparison with other available results in this area we show that, for sufficiently large d and k such that k ≤ d − 2, our fa...

Granular Pile Anchor (GPA) considers one of the solution foundation techniques, designed to mitigate the lifting of the sole resulting from expansive soils. This study work is to investigate the uplift movement response of (GPA) in expansive soil. The laboratory tests have been performed on an experimental. The effects of several parameters, such as length (L) of (GPA) and diameter (D), the thi...

Let ∆A(n, d) denote the largest possible average diameter of a bounded cell of a simple arrangement defined by n hyperplanes in dimension d. We have ∆A(n, 2) ≤ 2+ 2 n−1 in the plane, and ∆A(n, 3) ≤ 3+ 4 n−1 in dimension 3. In general, the average diameter of a bounded cell of a simple arrangement is conjectured to be less than the dimension; that is, ∆A(n, d) ≤ d. We propose an hyperplane arran...

Let G be connected simple graph with vertex set V(G) and edge set E(G). The diameter d(G), of G is defined as the maximum distance in G. 0 is said to be vertex diameter critical graph if d(G v) > d(G) for every v E V(G). Let 9(n, r, D) denote the class of r-regular, vertex critical graphs of diameter D on n vertices. Plesnik [16] conjectured that 9(n, r, D) * cP for every D ;::: 2 and r ;::: 2....

Introduction: Transient and disruption cavity sizes are fundamental parameters in the study of impact structures [1]. They are governed by the velocity, size and density of the impacting body, the target density and ambient gravitational acceleration. Hence, knowledge of transient and disruption cavity dimensions allows the calculation of energy release associated with impact. Since the recogni...

In a mixed (Δ, d)-regular graph, every vertex is incident with Δ ≥ 1 undirected edges and there are d ≥ 1 directed edges entering and leaving each vertex. If such a mixed graph has diameter 2, then its order cannot exceed (Δ+ d) + d+1. This quantity generalizes the Moore bounds for diameter 2 in the case of undirected graphs (when d = 0) and digraphs (when Δ = 0). For every d such that d − 1 is...

The diameter of a graph is an important factor for communication as it determines the maximum communication delay between any pair of processors in a network. Graham and Harary [N. Graham, F. Harary, Changing and unchanging the diameter of a hypercube, Discrete Applied Mathematics 37/38 (1992) 265–274] studied how the diameter of hypercubes can be affected by increasing and decreasing edges. Th...

Venturi injector is widely used in fertigation system due to its obvious advantages such as cheap and robust system without mobile pieces, simple structure, convenient to operation, stable performance, needless of external energy for operation etc. At present, the hydraulic parameters such as suction capacity (injection rate) for the most of the Venturi injectors produced domestically are not v...

For two vertices u and v in a graph G = (V, E), the detour distance D(u, v) is the length of a longest u–v path in G. A u–v path of length D(u, v) is called a u–v detour. A set S ⊆ V is called an edge detour set if every edge in G lies on a detour joining a pair of vertices of S. The edge detour number dn1(G) of G is the minimum order of its edge detour sets and any edge detour set of order dn1...

This paper presents 2-D finite volume method for computation of viscous drag based on Reynolds-averaged Navier-Stokes (RANS) equations. Computations are performed on bare submarine hull DREA and six axisymmetric bodies of revolution with a number of length-diameter (L/D) ratios ranging from 4 to 10. Both structured and unstructured grids are used to discretize the domain around the bodies. Diff...