Sharif Digital Repository

The energy of a graph is defined as the sum of absolute values of all eigenvalues of its adjacency matrix. For a nonempty graph G, S. Akbari, A. Alazemi, M. Andelić and M.A. Hosseinzadeh proposed a conjecture: The energy of the line graph of G is at least |E(G)|+Δ(G)−3, where E(G) is the edge set of G and Δ(G) is the maximum degree of G. In this paper, we give a proof confirming the conjecture, and present a lower bound and an upper bound for the energy of line graphs of regular graphs. © 2023 Elsevier Inc  

Pulsating heat pipe (PHP) is a type of wickless heat pipe that has a simple structure and an outstanding thermal performance. Nanofluid is a type of fluid in which nanoparticles are dispersed in a base fluid and have generally a better thermal conductivity in comparison with its base fluid. In this article, the performance of a nanofluid PHP is investigated. Graphene/water nanofluid with a concentration of 1 mg mL−1 and TiO2 (titania)/water nanofluid with a concentration of 10 mg mL−1 are used as the working fluids. To simultaneously investigate the thermal performance and flow regimes in the PHP, a one-turn copper PHP with a Pyrex glass attached to its adiabatic section is used. A one-turn... 

Pulsating heat pipe (PHP) is a type of wickless heat pipe that has a simple structure and an outstanding thermal performance. Nanofluid is a type of fluid in which nanoparticles are dispersed in a base fluid and have generally a better thermal conductivity in comparison with its base fluid. In this article, the performance of a nanofluid PHP is investigated. Graphene/water nanofluid with a concentration of 1 mg mL −1 and TiO 2 (titania)/water nanofluid with a concentration of 10 mg mL −1 are used as the working fluids. To simultaneously investigate the thermal performance and flow regimes in the PHP, a one-turn copper PHP with a Pyrex glass attached to its adiabatic section is used. A... 

Let G be a graph with a nonempty edge set, we denote the rank of the adjacency matrix of G and term rank of G, by rk (G) and Rk (G), respectively. van Nuffelen conjectured that for any graph G, χ (G) ≤ rk (G). The first counterexample to this conjecture was obtained by Alon and Seymour. In 2002, Fishkind and Kotlov proved that for any graph G, χ (G) ≤ Rk (G). Here we improve this upper bound and show that χl (G) ≤ (rk (G) + Rk (G)) / 2, where χl (G) is the list chromatic number of G. © 2006 Elsevier B.V. All rights reserved  

Let G be a graph with a nonempty edge set, we denote the rank of the adjacency matrix of G and the term rank of G, by rk (G) and Rk (G), respectively. It was conjectured [C. van Nuffelen, Amer. Math. Monthly 83 (1976) 265-266], for any graph G, χ (G) ≤ rk (G). The first counterexample to this conjecture was obtained by Alon and Seymour [J. Graph Theor. 13 (1989) 523-525]. Recently, Fishkind and Kotlov [Discrete Math. 250 (2002) 253-257] have proved that for any graph G, χ (G) ≤ Rk (G). In this Note we improve Fishkind-Kotlov upper bound and show that χ (G) ≤ rk(G)+Rk(G)/2. © 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved  

Numerous operational issues including voltage deviation and instability arise in distribution networks with insufficient reactive support. Static issues have been widely studied for years, and some dynamic ones are recently gaining attention due to the proliferation of distributed generation (DG). In this paper, a two-step reactive compensation planning procedure is proposed to address these challenges. In the first step, passive compensators are optimally sited and sized using a metaheuristic algorithm in order to improve steady-state indices including power efficiency, voltage profile, and static voltage stability. In the second step, a static synchronous compensator (Statcom) is located... 

Let G be a graph and for any natural number r, χs ′ (G, r) denotes the minimum number of colors required for a proper edge coloring of G in which no two vertices with distance at most r are incident to edges colored with the same set of colors. In [Z. Zhang, L. Liu, J. Wang, Adjacent strong edge coloring of graphs, Appl. Math. Lett. 15 (2002) 623-626] it has been proved that for any tree T with at least three vertices, χs ′ (T, 1) ≤ Δ (T) + 1. Here we generalize this result and show that χs ′ (T, 2) ≤ Δ (T) + 1. Moreover, we show that if for any two vertices u and v with maximum degree d (u, v) ≥ 3, then χs ′ (T, 2) = Δ (T). Also for any tree T with Δ (T) ≥ 3 we prove that χs ′ (T, 3) ≤ 2 Δ... 

The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all noncentral elements of R, and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this article we investigate some graph-theoretic properties of Γ(Mn(F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GLn(F) and SLn(F). We show that Γ(Mn(F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GLn(F)) and Γ(SL n(F)). Also we show... 

An Artificial Neural Network (ANN) model has been designed for predicting the effects of alloying elements (Fe, Si, Al, Mn) on the recrystallization behavior and microstructural changes of 70/30 brass. The model introduced here considers the content of alloying elements, temperature, and time of recrystallization as inputs while percent of recrystallization is presented as output. It is shown that the designed model is able to predict the effect of alloying elements well. It is also shown that all alloying elements strongly affect the recrytallization kinetics, and all slow down the recrystallization process. The effect of alloying elements on the activation energy for recrystallization has... 

A subgraph in an edge-colored graph is multicolored if all its edges receive distinct colors. In this paper, we prove that a complete graph on 2m (m ≠ 2) vertices K2m can be properly edge-colored with 2m - 1 colors in such a way that the edges of K2m can De partitioned into m multicolored isomorphic spanning trees. © 2006 Society for Industrial and Applied Mathematics  

Packet loss recovery is an important part of P2P video streaming networks due to inevitable packet loss in today's internet and interdependency of data units in compressed video streams. In addition, the architecture of P2P streaming networks, in which the data delivered to the receivers through chain of peers, can intensify the impact of the internet packet loss on the quality of perceived video at the receivers. FEC and ARQ are the two most important techniques that can be used to overcome the side effect of the internet packet loss in P2P video streaming networks. Based on these two techniques, different packet loss recovery strategies can be applied in different overlay hops of a given... 

Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G,x)=σi=1 nd(G,i)xi, where d(G,i) is the number of dominating sets of G of size i. A root of D(G,x) is called a domination root of G. We denote the set of distinct domination roots by Z(D(G,x)). Two graphs G and H are said to be D-equivalent, written as G~H, if D(G,x)=D(H,x). The D-equivalence class of G is [G]={H:H~G}. A graph G is said to be D-unique if [G]={G}. In this paper, we show that if a graph G has two distinct domination roots, then Z(D(G,x))={-2,0}. Also, if G is a graph with no pendant vertex and has three distinct domination roots, then Z(D(G,x)). Also, we study the D-equivalence classes of... 

Let R be a ring with identity and M be a unitary left R-module. The intersection graph of submodules of M, denoted by G(M), is defined to be a graph whose vertices are in one to one correspondence with all non-trivial submodules of M and two distinct vertices are adjacent if and only if the corresponding submodules of M have non-zero intersection. In this paper, we consider the intersection graph of submodules of a module. We determine the structure of modules whose clique numbers are finite. We show that if 1 < ω(G(M)) < ∞, then M is a direct sum of a finite module and a cyclic module, where ω(G(M)) denotes the clique number of G(M). We prove that if ω(G(M)) is not finite, then M contains... 

Peer-to-peer streaming has recently gained attention as an effective solution to support large scale media streaming applications over the Internet. One of the main challenges of peer-to-peer video streaming is the cumulative impact of the Internet packet loss due to the decoding dependency of the compressed video frames. In this paper we study the impact of the Internet packet loss on the performance of peer-to-peer video streaming systems, and analyze the efficiency of various packet loss recovery policies in such systems. Our analytical and simulation results show how the Internet packet loss can affect the performance of peer- to-peer video streaming systems and how different packet loss... 

In this paper we propose a rate-efficient peer-to-peer architecture for video multicasting over the Internet. The limited capacity of the Internet hosts and the heterogeneous property of their access links are the main challenges of the peer-to-peer video multicasting over the Internet. Although, the rate-optimized overlay tree construction is a NP-hard problem, we propose a number of distributed and efficient protocols for rate-efficient overlay tree construction. Our proposed protocols include efficient join, improvement, overlay tree refinement and an optimum rate allocation protocol. The simulation results show the efficiency of the proposed protocols in rate-efficient overlay tree... 

A t-(v, k, λ) design D = (X, B) with B = Pk(X) is called a full design. For t = 2, k; = 3 and any v, we give minimal defining sets for these designs. For v = 6 and v = 7, smallest defining sets are found  

In this paper, a new dynamic proxy solution based on overlay multicasting network for layered video streaming is presented. In our proposed approach, all clients in an Internet service provider network interested in receiving a video stream, provided by a media server in the Internet, organize themselves into an overlay tree. The root of the overlay tree acts as a proxy and receives video stream from original server and distributes it in the local overlay tree. In addition to introducing a new architecture, our main contribution in this paper is proposing a number of distributed protocols for construction and improvement of local overlay tree in video streaming applications. The experimental... 

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,... 

Let μm be the group of mth roots of unity. In this paper it is shown that if m is a prime power, then the number of all square matrices (of any order) over μm with non-zero constant determinant or permanent is finite. If m is not a prime power, we construct an infinite family of matrices over μm with determinant one. Also we prove that there is no n×n matrix over μp with vanishing permanent, where p is a prime and n = pα-1. © 2003 Elsevier Inc. All rights reserved  

A signed graph Γ is said to be determined by its spectrum if every signed graph with the same spectrum as Γ is switching isomorphic with Γ. Here it is proved that the path Pn, interpreted as a signed graph, is determined by its spectrum if and only if n≡0,1, or 2 (mod 4), unless n∈{8,13,14,17,29}, or n=3. © 2018 Elsevier Inc