Let $x$ and $y$ be two distinct vertices in a connected graph $G$. The $x,y$-location of a vertex $w$ is the ordered pair of distances from $w$ to $x$ and $y$, that is, the ordered pair $(d(x,w), d(y,w))$. A set of vertices $W$ in $G$ is $x,y$-located if any two vertices in $W$ have distinct $x,y$-location.A set $W$ of vertices in $G$ is 2-located if it is $x,y$-located, for some distinct...

two-dimensional electrophoresis (2-d electrophoresis) is a powerful and extensively used method for analysis of complex protein mixtures extracted from cells, tissue, or other biological samples such as helminth parasites including, f. hepatica. each spot on the resulting two-dimensional collection corresponds to a single protein species in the sample. this study was carried out to detect of gs...

Let Γ=(V,E) be a graph and ‎W_(‎a)={w_1,…,w_k } be a subset of the vertices of Γ and v be a vertex of it. The k-vector r_2 (v∣ W_a)=(a_Γ (v,w_1),‎…‎ ,a_Γ (v,w_k)) is the adjacency representation of v with respect to W in which a_Γ (v,w_i )=min{2,d_Γ (v,w_i )} and d_Γ (v,w_i ) is the distance between v and w_i in Γ. W_a is called as an adjacency resolving set for Γ if distinct vertices of ...

Abstract The Cremona conjecture, also called Jacobi problem, claims that a polynomial morphism $${{\mathbb C}^n \longrightarrow {\mathbb C}^n}$$ C n ⟶ is invertible as if its Jacobian constant and not zero. In this paper, we show ...