We determine that the connectivity and the edgeconnectivity of the Cartesian product G1 × G2 of two strongly connected and finite digraphs G1 and G2 are equal to min{n1κ2,n2κ1, δ+ 1 + δ+ 2 , δ− 1 + δ− 2 } and min{n1λ2,n2λ1, δ+ 1 + δ+ 2 , δ− 1 + δ− 2 }, respectively, where ni , κi , λi , δ + i , δ − i are the order, the connectivity, the edgeconnectivity, the minimum out-degree and the minimum i...

Use vi , i , i , i to denote order, connectivity, edge-connectivity and minimum degree of a graphGi for i=1, 2, respectively. For the connectivity and the edge-connectivity of the Cartesian product graph, up to now, the best results are (G1×G2) 1+ 2 and (G1×G2) 1+ 2. This paper improves these results by proving that (G1×G2) min{ 1+ 2, 2+ 1} and (G1×G2)= min{ 1+ 2, 1v2, 2v1} ifG1 andG2 are conne...

For an ordered k-decomposition D = {G1, G2,...,Gk} of a connected graph G (V,E), the D-representation edge e is k-tuple γ(e/D)=(d(e, G1), d(e, G2), ...,d(e, Gk)), where Gi) represents distance from to Gi. A decomposition resolving if every two distinct edges have representations. The minimum k for which has its dimension dec(G). In this paper, corona product path Pn and cycle Cn with complete g...

For arbitrary graphs G1 and G2, define the Ramsey number R(G1,G2) to be the minimum positive integer N such that in every bicoloring of edges of the complete graph KN with, say, red and blue colors, there is either a red copy of G1 or a blue copy of G2. The classical Ramsey number r(k, l) is in our terminology R(Kk,Kl). Call a family F of graphs linear Ramsey if there exists a constant C = C(F)...

Definition(s): Let G = (V,E) be a graph. A set S ⊆ V is called separating in G if G− S is not connected. The connectivity of G, written κ(G), is the minimum size of a set S, such that G−S is not connected or has only one vertex. A separating set in G with cardinality κ(G) is called a κ-set in G. Let G1 = (V1, E1) and G2 = (V2, E2) be a graphs. Strong product G1 G2 of graphs G1 and G2 is the gra...

Crossbred pigs (n=120) from Duroc sires mated to Landrace x Large White dams, with a mean BW of 110.5+/-2.3 kg, were used to investigate the effect of increasing the slaughter weight of gilts with regard to that of the barrows on the production of high quality dry-cured hams from Spain (Teruel ham). There were 3 treatments: barrows slaughtered at 130 kg of BW (B), gilts slaughtered at 130 kg of...

Let G be a connected graph and g non-negative integer. A vertex set S of is called g-extra cut if G−S disconnected each component has at least g+1 vertices. The connectivity the minimum cardinality one cut. For two graphs G1=(V1,E1) G2=(V2,E2), strong product G1⊠G2 defined as follows: its V1×V2 edge {(x1,x2)(y1,y2)|x1=x2 y1y2∈E2; or y1=y2 x1x2∈E1; x1x2∈E1 y1y2∈E2}, where (x1,x2),(y1,y2)∈V1×V2. ...

We use a technique based on matroids to construct two nonzero patterns Z1 and Z2 such that the minimum rank of matrices described by Z1 is less over the complex numbers than over the real numbers, and the minimum rank of matrices described by Z2 is less over the real numbers than over the rational numbers. The latter example provides a counterexample to a conjecture in [AHKLR] about rational re...

Objective: To analyze the obstetric and neonatal outcomes in pregnancies after Roux-en-Y Gastric Bypass (RYGB) compared with matched control pregnancies. Methodology: A cross-sectional study of the analytical type with pregnant women matched by age and pre-pregnancy body mass index (BMI) was carried out. Group 1 (G1) comprised 60 pregnant women who did not previously undergo RYGB and Group 2 (G...

For an ordered set { } k w w w W , , , 2 1  = of vertices and a vertex v in a connected graph G, the (metric) representation of v with respect to W is the k-vector r(v/W) = (d(v, w1), d(v, w2), ..., d(v, wk)), where d(x, y)representsthe distance between the vertices x and y. A resolving set of minimum cardinality is called a minimum resolving set or abasis and the cardinality of a basis for G ...