Sharif Digital Repository

A vector is called nowhere-zero if it has no zero entry. In this article we search for graphs with nowhere-zero eigenvectors. We prove that distance-regular graphs and vertex-transitive graphs have nowhere-zero eigenvectors for all of their eigenvalues and edge-transitive graphs have nowhere-zero eigenvectors for all non-zero eigenvalues. Among other results, it is shown that a graph with three distinct eigenvalues has a nowhere-zero eigenvector for its smallest eigenvalue  

Let A be a Hermitian matrix whose graph is G (i.e. there is an edge between the vertices i and j in G if and only if the (i,j) entry of A is non-zero). Let λ be an eigenvalue of A with multiplicity mA(λ). An edge e=ij is said to be Parter (resp., neutral, downer) for λ,A if mA(λ)-mA-e(λ) is negative (resp., 0, positive ), where A-e is the matrix resulting from making the (i,j) and (j,i) entries of A zero. For a tree T with adjacency matrix A a subset S of the edge set of G is called an edge star set for an eigenvalue λ of A, if |S|=mA(λ) and A-S has no eigenvalue λ. In this paper the existence of downer edges and edge star sets for non-zero eigenvalues of the adjacency matrix of a tree is... 

In this paper we study graphs all of whose star sets induce cliques or co-cliques. We show that the star sets of every tree for each eigenvalue are independent sets. Among other results it is shown that each star set of a connected graph G with three distinct eigenvalues induces a clique if and only if G = K1, 2 or K2, ..., 2. It is also proved that stars are the only graphs with three distinct eigenvalues having a star partition with independent star sets. © 2008 Elsevier Inc. All rights reserved  

Let G be a graph. A spanning subgraph of G is called a {1, 2}-factor if each of its components is a regular graph of degree one or two. In this paper we provide a short proof of a theorem of Tutte which says that a graph G has a {1, 2}-factor if and only if i(GS) ≤ |S| for any S ⊆ V(G), where i(GS) denotes the number of isolated vertices of GS  

One of the most important systems for providing anonymous communication is the Mix nets which should provide correctness and privacy as security requirements against active adversaries. In 2009, Zhong proposed a new mix net scheme which uses identity-based cryptographic techniques and proved that it has 'correctness' and 'privacy' properties in the semi-honest model. Since the semi-honest model is a very strong assumption for practical application, we show that if a user or the last mix server is corrupted, Zhong scheme does not provide privacy against an active adversary  

For the efficient removal of some anionic dyes, a novel adsorbent was developed. The adsorbent was prepared by coating a synthetic polymer on magnetite nanosphere surface as a magnetic carrier. The synthesized nano-adsorbent was fully characterized using Fourier transform infrared spectroscopy (FT-IR), vibrating sample magnetometer, X-ray diffractometer, scanning electron microscope, and transmission electronic microscopy measurements. The synthesized nano-adsorbent showed high adsorption capacity towards removal of some anionic dyes (221.4, 201.6, and 135.3 mg g-1 for reactive red 195, reactive yellow 145, and reactive blue 19 dye, respectively) from aqueous samples. The dye adsorption was... 

Let G be a simple graph of order n and size m which is not a tree. If ℓ; ≤ 3 is a natural number and the length of every cycle of G is divisible by ℓ, then m ≤l/l-2 (n -2), and the equality holds if and only if the following hold: (i) ℓ is odd and G is a cycle of order ℓ or (ii) ℓ is even and G is a generalized 6>-graph with paths of length |l/2 It is shown that for a (0 mod ℓ)-cycle graph, m/n < l/l-1 if ℓ is odd, and for a given e > 0, there exists a (0 mod ℓ)-cycle graph G with m/n > l/l-2 - e. Also m/n > l/l-2 if ℓ is even, and for a given e > 0, there exists a (0 mod ℓ)-cycle graph G with m/n l/l-2-e  

For a graph G, a zero-sum flow is an assignment of non-zero real numbers on the edges of G such that the total sum of all edges incident with any vertex of G is zero. A zero-sumk -flow for a graph G is a zero-sum flow with labels from the set {± 1, ..., ± (k - 1)}. In this paper for a graph G, a necessary and sufficient condition for the existence of zero-sum flow is given. We conjecture that if G is a graph with a zero-sum flow, then G has a zero-sum 6-flow. It is shown that the conjecture is true for 2-edge connected bipartite graphs, and every r-regular graph with r even, r > 2, or r = 3. © 2009 Elsevier Inc. All rights reserved  

Bacterial cellulose (BC) is an extracellular natural polymer produced by many microorganisms and its properties could be tailored via specific fabrication methods and culture conditions. There is a growing interest in BC derived materials due to the main features of BC such as porous fibrous structure, high crystallinity, impressive physico-mechanical properties, and high water content. However, pristine BC lacks some features, limiting its practical use in varied applications. Thus, fabrication of BC composites has been attempted to overcome these constraints. This review article overviews most recent advance in the development of BC composites and their potential in biomedicine including...