ABSTRACT: A difference labeling of a graph G is realized by assigning distinct integer values to its vertices and then associating with each edge the absolute difference of those values assigned to its end vertices. A decomposition of labeled graph into parts, each part containing the edge having a commonweight is called a common – weight decomposition. In this paper we investigate the existenc...

Complete row and column symmetry breaking in constraint models using the lex leader method is generally prohibitively costly. Double lex, which is derived from lex leader, is commonly used in practice as an incomplete symmetrybreaking method for row and column symmetries. Double lex is based on a rowwise canonical variable ordering. However, this choice is arbitrary. We investigate other canoni...

We give a new proof of a recent inequality for bicentric quadrilaterals that is an extension of the Euler-like inequality R ≥ √ 2r. A bicentric quadrilateral ABCD is a convex quadrilateral that has both an incircle and a circumcircle. In [6], Zhang Yun called these “double circle quadrilaterals” and proved that

Converting a quadrilateral input mesh into a C surface with one bi-3 tensorproduct spline patch per facet is a classical challenge. We give explicit local averaging formulas for the spline control points. Where the quadrilateral mesh is not regular, the patches have two internal double knots, the least number and multiplicity to always allow for an unbiased G construction.

In this paper, we have shown that collection of paths P i n where n is odd, cycle, triangular snake, quadrilateral snake, P 2 n are even sequential harmonious graph and also we prove that the cycle Cn be a cycle u1, u2, · · · , un is an even sequential harmonious graph. Let G be a graph with V (G) = V (Cn) ∪ {wi : 1 ≤ i ≤ n}, E(G) = E(Cn) ∪ {uiwiui−1wi : 1 ≤ i ≤ n}, then G is an even sequential...

In this paper, double integrals over an arbitrary quadrilateral are evaluated exploiting finite element method. The physical region is transformed into a standard quadrilateral finite element using the basis functions in local space. Then the standard quadrilateral is subdivided into two triangles, and each triangle is further discretized into 4 n right isosceles triangles, with area 1 2n2, and...