Sharif Digital Repository

A bipartite graph G = (A,B,E) is convex on B if there exists an ordering of the vertices of B such that for any vertex v ? A, vertices adjacent to v are consecutive in B. A complete bipartite subgraph of a graph G is called a biclique of G. Motivated by an application to analyzing DNA microarray data, we study the problem of finding maximum edge bicliques in convex bipartite graphs. Given a bipartite graph G = (A,B,E) which is convex on B, we present a new algorithm that computes a maximum edge biclique of G in O(nlog3 n log log n) time and O(n) space, where n = |A|. This improves the current O(n 2) time bound available for the problem. We also show that for two special subclasses of convex... 

A tree containing exactly two non-pendant vertices is called a doublestar. A double-star with degree sequence (k1 +1, k2 +1, 1, ⋯ , 1) is denoted by Sk1,k2 . We study the edge-decomposition of graphs into double-stars. It was proved that every double-star of size k decomposes every 2k-regular graph. In this paper, we extend this result by showing that every graph in which every vertex has degree 2k + 1 or 2k + 2 and containing a 2-factor is decomposed into Sk1,k2 and Sk1-1,k2 , for all positive integers k1 and k2 such that k1 + k2 = k  

Let R be a commutative ring with identity, and let A(R) be the set of ideals with non-zero annihilator. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R)* = A(R) {0}, and two distinct vertices I and J are adjacent if and only if IJ = 0. In this paper, we study some connections between the graph theoretic properties of this graph and some algebraic properties of a commutative ring. We prove that if AG(R) is a tree, then either AG(R) is a star graph or a path of order 4 and, in the latter case, R = F × S, where F is a field and S is a ring with a unique non-trivial ideal. Moreover, we prove that if R has at least three minimal prime ideals, then AG(R) is... 

Let G = (V,E) be a simple undirected graph. For a given set L ⊂ ℝ, a function ω: E → L is called an L-flow. Given a vector γ ∈ ℝv, ω is a γ-L-flow if for each υ ∈ V, the sum of the values on the edges incident to υ is γ(υ). If γ(υ) = c, for all υ ∈ V, then the γ-L-flow is called a c-sum L-flow. In this paper, the existence of γ-L-flows for various choices of sets L of real numbers is studied, with an emphasis on 1-sum flows. Let L be a subset of real numbers containing 0 and denote L*:= L {0}. Answering a question from [S. Akbari, M. Kano, and S. Zare. A generalization of 0-sum flows in graphs. Linear Algebra Appl., 438:3629-3634, 2013.], the bipartite graphs which admit a 1-sum ℝ*-flow or... 

Let Γ(R) be the zero-divisor graph of a commutative ring R. An interesting question was proposed by Anderson, Frazier, Lauve, and Livingston: For which finite commutative rings R is Γ (R) planar? We give an answer to this question. More precisely, we prove that if R is a local ring with at least 33 elements, and Γ(R) ≠ 0, then Γ(R) is not planar. We use the set of the associated primes to find the minimal length of a cycle in Γ(R). Also, we determine the rings whose zero-divisor graphs are complete r-partite graphs and show that for any ring R and prime number p, p ≥ 3, if Γ(R) is a finite complete p-partite graph, then Z(R) = p2, R = p3, and R is isomorphic to exactly one of the rings ℤp3,... 

Recommender systems have become an important issue in network science. Collaborative filtering and its variants are the most widely used approaches for building recommender systems, which have received great attention in both academia and industry. In this paper, we studied the relationship between recommender systems and connectivity of users-items bipartite network. This results in a novel recommendation algorithm. In our method recommended items are selected based on the eigenvector corresponding to the algebraic connectivity of the graph - the second smallest eigenvalue of the Laplacian matrix. Since recommending an item to a user equals to adding a new link to the users-items bipartite... 

Let G be a graph and H be an abelian group. For every subset SH a map φ:E(G)→S is called an S-flow. For a given S-flow of G, and every v∈V(G), define s(v)=∑uv∈E(G)φ(uv). Let k∈H. We say that a graph G admits a k-sum S-flow if there is an S-flow such that for each vertex v,s(v)=k. We prove that if G is a connected bipartite graph with two parts X={x1,⋯,xr}, Y={y1,⋯, ys} and c1,⋯,cr,d1,⋯, ds are real numbers, then there is an R-flow such that s( xi)=ci and s(yj)=dj, for 1≤i≤r,1≤j≤s if and only if ∑i=1rci=∑j=1s dj. Also, it is shown that if G is a connected non-bipartite graph and c1,⋯,cn are arbitrary integers, then there is a Z-flow such that s(vi)=ci, for i=1, ⋯,n if and only if the number... 

We study the role of correlation in mechanisms of energy exchange between an interacting bipartite quantum system and its environment by decomposing the energy of the system to local and correlation-related contributions. When the system Hamiltonian is time independent, no external work is performed. In this case, energy exchange between the system and its environment occurs only due to the change in the state of the system. We investigate the possibility of a special case where the energy exchange with the environment occurs exclusively due to changes in the correlation between the constituent parts of the bipartite system, while their local energies remain constant. We find sufficient... 

We consider two ensembles of qubits dissipating into two overlapping environments, that is, with a certain number of qubits in common that dissipate into both environments. We then study the dynamics of bipartite entanglement between the two ensembles by excluding the common qubits. To get analytical solutions for an arbitrary number of qubits we consider initial states with a single excitation and show that the largest amount of entanglement can be created when excitations are initially located among side (noncommon) qubits. Moreover, the stationary entanglement exhibits a monotonic (nonmonotonic) scaling versus the number of common (side) qubits  

For every h ∈ ℕ, a graph G with the vertex set V (G) and the edge set E(G) is said to be h-magic if there exists a labeling l: E(G) → ℤh{0} such that the induced vertex labeling s: V (G) → ℤh, defined by s(v) = Puv∈E(G) l(uv) is a constant map. When this constant is zero, we say that G admits a zero-sum h-magic labeling. The null set of a graph G, denoted by N(G), is the set of all natural numbers h ∈ ℕ such that G admits a zero-sum h-magic labeling. In 2012, the null sets of 3-regular graphs were determined. In this paper we show that if G is an r-regular graph, then for even r (r > 2), N(G) = ℕ and for odd r (r ≠ 5), ℕ {2, 4} ⊆ N(G). Moreover, we prove that if r is odd and G is a 2-edge... 

Measuring centrality in a social network, especially in bipartite mode, poses many challenges, for example, the requirement of full knowledge of the network topology, and the lack of properly detecting top-kbehavioral representative users. To overcome the above mentioned challenges, we propose HellRank, an accurate centrality measure for identifying central nodes in bipartite social networks. HellRank is based on the Hellinger distance between two nodes on the same side of a bipartite network. We theoretically analyze the impact of this distance on a bipartite network and find upper and lower bounds for it. The computation of the HellRank centrality measure can be distributed, by letting... 

Observability of complex systems/networks is the focus of this paper, which is shown to be closely related to the concept of contraction. Indeed, for observable network tracking it is necessary/sufficient to have one node in each contraction measured. Therefore, nodes in a contraction are equivalent to recover for loss of observability, implying that contraction size is a key factor for observability recovery. Here, developing a polynomial order contraction detection algorithm, we analyze the distribution of contractions, studying its relation with key network properties. Our results show that contraction size is related to network clustering coefficient and degree heterogeneity.... 

Let γs′ (G) be the signed edge domination number of G. In 2006, Xu conjectured that: for any 2-connected graph G of order n (n ≥ 2), γs′ (G) ≥ 1. In this article we show that this conjecture is not true. More precisely, we show that for any positive integer m, there exists an m-connected graph G such that γs′ (G) ≤ - frac(m, 6) | V (G) |. Also for every two natural numbers m and n, we determine γs′ (Km, n), where Km, n is the complete bipartite graph with part sizes m and n. © 2008 Elsevier B.V. All rights reserved  

We propose a scheme for distillation of free bipartite entanglement from bipartite bound entangled states. The crucial element of our scheme is an ancillary system that is coupled to the initial bound entangled state via appropriate weak measurements. We show that in this protocol free entanglement can be always generated with nonzero probability by using a single copy of the bound entangled state. We also derive a lower bound on the entanglement cost of the protocol and conclude that, on average, applying weaker measurements results in relatively higher values of free entanglement as well as lower costs  

We say that two graphs G1 and G2 with the same vertex set commute if their adjacency matrices commute. In this paper, we find all integers n such that the complete bipartite graph Kn, n is decomposable into commuting perfect matchings or commuting Hamilton cycles. We show that there are at most n - 1 linearly independent commuting adjacency matrices of size n; and if this bound occurs, then there exists a Hadamard matrix of order n. Finally, we determine the centralizers of some families of graphs. © 2008 Elsevier B.V. All rights reserved