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graph-theory
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Computing ABC4 index of nanostar dendrimers
, Article Optoelectronics and Advanced Materials, Rapid Communications ; Volume 4, Issue 9 , 2010 , Pages 1419-1422 ; 18426573 (ISSN) ; Hosseinzadeh, M. A ; Sharif University of Technology
2010
Abstract
The ABC index is a topological index was defined as where dG(u) denotes degree of vertex u. Now we define a new version of ABC index as where The goal of this paper is further the study of the ABC4 index
On the Zagreb indices of nanostar dendrimers
, Article Optoelectronics and Advanced Materials, Rapid Communications ; Volume 4, Issue 3 , 2010 , Pages 378-380 ; 18426573 (ISSN) ; Ghorbani, M ; Sharif University of Technology
2010
Abstract
Let G be a graph. The first and second Zagreb index of G is defined as M1(G)= Σ degG(V)2 and M2(G)= Σ degG(u)degG(V) respectively. In this paper we compute Zagreb indices of chain graphs
A note on graceful graphs with large chromatic numbers
, Article Ars Combinatoria ; Volume 90 , 2009 , Pages 423-424 ; 03817032 (ISSN) ; Sharif University of Technology
2009
Abstract
A graceful labeling of a graph G with m edges is a function f : V(G) → {0,⋯, m} such that distinct vertices receive distinct numbers and {|f(u) - f(v)| : uv ∈ E(G)} = {1,⋯, m}. A graph is graceful if it has a graceful labeling. In [1] this question was posed: "Is there an n-chromatic graceful graph for n ≥ 6?". In this paper it is shown that for any natural number n, there exists a graceful graph G with χ(G) = n
Distribution function of the shortest path in networks of queues
, Article OR Spectrum ; Volume 27, Issue 1 , 2005 , Pages 123-144 ; 01716468 (ISSN) ; Modarres, M ; Sharif University of Technology
2005
Abstract
In this paper, we consider acyclic networks of queues as a model to support the design of a dynamic production system. Each service station in the network represents a manufacturing or assembly operation. Only one type of product is produced by the system, but there exist several distinct production processes for manufacturing this product, each one corresponding with a directed path in the network of queues. In each network node, the number of servers in the corresponding service station is either one or infinity. The service time in each station is either exponentially distributed or belongs to a special class of Coxian distribution. Only in the source node, the service system may be...
Structural covariance of superficial white matter in mild Alzheimer's disease compared to normal aging
, Article Brain and Behavior ; Vol. 4, issue. 5 , September , 2014 , p. 721-737 ; Fornari, E ; Jalili, M ; Meuli, R ; Knyazeva, M. G ; Sharif University of Technology
Abstract
Introduction: Interindividual variations in regional structural properties covary across the brain, thus forming networks that change as a result of aging and accompanying neurological conditions. The alterations of superficial white matter (SWM) in Alzheimer's disease (AD) are of special interest, since they follow the AD-specific pattern characterized by the strongest neurodegeneration of the medial temporal lobe and association cortices. Methods: Here, we present an SWM network analysis in comparison with SWM topography based on the myelin content quantified with magnetization transfer ratio (MTR) for 39 areas in each hemisphere in 15 AD patients and 15 controls. The networks are...
Identifying brain functional connectivity alterations during different stages of alzheimer’s disease
, Article International Journal of Neuroscience ; 2020 ; Fatemizadeh, E ; Motie-Nasrabadi, A ; Sharif University of Technology
Taylor and Francis Ltd
2020
Abstract
Purpose: Alzheimer's disease (AD) starts years before its signs and symptoms including the dementia become apparent. Diagnosis of the AD in the early stages is important to reduce the speed of brain decline. Aim of the study: Identifying the alterations in the functional connectivity of the brain during the disease stages is among the main important issues in this regard. Therefore, in this study, the changes in the functional connectivity during the AD stages were analyzed. Materials and methods: By employing the functional magnetic resonance imaging (fMRI) data and graph theory, weighted undirected graphs of the whole-brain and default mode network (DMN) network were investigated...
Induced path factors of regular graphs
, Article Journal of Graph Theory ; Volume 97, Issue 2 , 2021 , Pages 260-280 ; 03649024 (ISSN) ; Horsley, D ; Wanless, I. M ; Sharif University of Technology
John Wiley and Sons Inc
2021
Abstract
An induced path factor of a graph (Formula presented.) is a set of induced paths in (Formula presented.) with the property that every vertex of (Formula presented.) is in exactly one of the paths. The induced path number (Formula presented.) of (Formula presented.) is the minimum number of paths in an induced path factor of (Formula presented.). We show that if (Formula presented.) is a connected cubic graph on (Formula presented.) vertices, then (Formula presented.). Fix an integer (Formula presented.). For each (Formula presented.), define (Formula presented.) to be the maximum value of (Formula presented.) over all connected (Formula presented.) -regular graphs (Formula presented.) on...
Induced path factors of regular graphs
, Article Journal of Graph Theory ; Volume 97, Issue 2 , 2021 , Pages 260-280 ; 03649024 (ISSN) ; Horsley, D ; Wanless, I. M ; Sharif University of Technology
John Wiley and Sons Inc
2021
Abstract
An induced path factor of a graph (Formula presented.) is a set of induced paths in (Formula presented.) with the property that every vertex of (Formula presented.) is in exactly one of the paths. The induced path number (Formula presented.) of (Formula presented.) is the minimum number of paths in an induced path factor of (Formula presented.). We show that if (Formula presented.) is a connected cubic graph on (Formula presented.) vertices, then (Formula presented.). Fix an integer (Formula presented.). For each (Formula presented.), define (Formula presented.) to be the maximum value of (Formula presented.) over all connected (Formula presented.) -regular graphs (Formula presented.) on...
Longest path in networks of queues in the steady-state
, Article International Journal of Engineering, Transactions A: Basics ; Volume 17, Issue 1 , 2004 , Pages 33-50 ; 17281431 (ISSN) ; Modarres, M ; Sharif University of Technology
National Research Center of Medical Sciences
2004
Abstract
Due to the importance of longest path analysis in networks of queues, we develop an analytical method for computing the steady-state distribution function of longest path in acyclic networks of queues. We assume the network consists of a number of queuing systems and each one has either one or infinite servers. The distribution function of service time is assumed to be exponential or Erlang. Furthermore, the source node can include an M/G/∞ queuing system. The length of the arcs connecting the nodes of the network is assumed to be independent random variables. In the proposed method, the network of queues is transformed into a relevant stochastic network. Then, we compute the distribution...
Reaction-diffusion models describing a two-lane traffic flow
, Article Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics ; Volume 62, Issue 5 , 2000 , Pages 5940-5947 ; 1063651X (ISSN) ; Sharif University of Technology
2000
Abstract
A unidirectional two-lane road is approximated by a set of two parallel closed one-dimensional chains. Two types of cars, i.e., slow and fast ones are considered in the system. Based on the Nagel-Schreckenberg model of traffic flow [K. Nagel and M. Schreckenberg, J. Phys. 2, 2221 (1992)], a set of reaction-diffusion processes is introduced to simulate the behavior of the cars. Fast cars can pass the slow ones using the passing lane. We write and solve the mean-field rate equations for the density of slow and fast cars, respectively. We also investigate the properties of the model through computer simulations and obtain the fundamental diagrams. A comparison between our results and the...
Combinatorial Curvature of Graphs
, M.Sc. Thesis Sharif University of Technology ; Daneshgar, Amir (Supervisor) ; Javadi Jourtani, Ramin (Supervisor)
Abstract
There are a variety of notions of curvature that one could define on graphs. In this thesis, we introduce one of them which is called the ”Combinatorial Curvature”. This curvature is defined on graphs embedded on a surface, however as the name suggests,the combinatorial curvature of a vertex depends only on the combinatorial properties of the graph, and not on the geometric properties of the surface on which the graph is embedded. More precisely, the combinatorial curvature of a vertex is a function of the degree of the vertex and the faces which are incident to that vertex.In the main part of this thesis, we have tried to collect the most important results about the combinatorial curvature....
Risk of attack coefficient effect on availability of Ad-hoc networks
, Article 2011 IEEE Consumer Communications and Networking Conference, CCNC'2011, Las Vegas, NV, 8 January 2011 through 11 January 2011 ; 2011 , Pages 166-168 ; 9781424487905 (ISBN) ; Farhat, F ; Pakravan, M. R ; Aref, M. R ; Sharif University of Technology
2011
Abstract
Security techniques have been designed to obtain certain objectives. One of the most important objectives all security mechanisms try to achieve is the availability, which insures that network services are available to various entities in the network when required. But there has not been any certain parameter to measure this objective in network. In this paper we consider availability as a security parameter in ad-hoc networks. However this parameter can be used in other networks as well. We also present the connectivity coefficient of nodes in a network which shows how important is a node in a network and how much damage is caused if a certain node is compromised
Tutte Conjecture on Nowhere-zero Flow
, M.Sc. Thesis Sharif University of Technology ; Akbari, Saeed (Supervisor)
Abstract
In this thesis, the notion of nowhere-zero flow on graphs in defined with values is an Abelian group. It is shown that the existence of nowhere-zero flow with values in H depends on only the cardinal of H. Also the existence of nowhere-zero flowwith values on Zk is equivalent to the existence of the nowhere-zero flow with values in the set 1,2,...,k-1 on group Z.It is a easily seen that the nowhere zero flow on the graph with bridge doesn’t exist. Also has been proved any graph with no bridge has nowhere-zero 6 flow.Concidentally, the existence of nowhere-zero 5 flow for graphs with no bridge isstill an open problem.In 3-flow case, recently it is shown that any 8-edge connected graph has...
A polynomial time branch and bound algorithm for the single item economic lot sizing problem with all units discount and resale [electronic resource]
, Article International Journal of Optimization in Civil Engineering ; 2012, 2(2): 183-202 ; Shadrokh, Sh ; Eshghi, Kourosh ; Sharif University of Technology
Abstract
The purpose of this paper is to present a polynomial time algorithm which determines the lot sizes for purchase component in Material Requirement Planning (MRP) environments with deterministic time-phased demand with zero lead time. In this model, backlog is not permitted, the unit purchasing price is based on the all-units discount system and resale of the excess units is possible at the ordering time. The properties of an optimal order policy are argued and on the basis of them, a branch and bound algorithm is presented to construct an optimal sequence of order policies. In the proposed B&B algorithm, some useful fathoming rules have been proven to make the algorithm very efficient. By...
Hemispheric asymmetry of electroencephalography-based functional brain networks
, Article NeuroReport ; Volume 25, Issue 16 , 12 November , 2014 , Pages 1266-1271 ; ISSN: 09594965 ; Sharif University of Technology
Abstract
Electroencephalography (EEG)-based functional brain networks have been investigated frequently in health and disease. It has been shown that a number of graph theory metrics are disrupted in brain disorders. EEG-based brain networks are often studied in the whole-brain framework, where all the nodes are grouped into a single network. In this study, we studied the brain networks in two hemispheres and assessed whether there are any hemispheric-specific patterns in the properties of the networks. To this end, resting state closed-eyes EEGs from 44 healthy individuals were processed and the network structures were extracted separately for each hemisphere. We examined neurophysiologically...
Hyper-T-width and hyper-D-width: Stable connectivity measures for hypergraphs
, Article Theoretical Computer Science ; Volume 463 , 2012 , Pages 26-34 ; 03043975 (ISSN) ; Sharif University of Technology
2012
Abstract
We introduce hyper-D-width and hyper-T-width as the first stable (see Definition 3) measures of connectivity for hypergraphs. After studying some of their properties and, in particular, proposing an algorithm for computing nearly optimal hyper-T-decomposition when hyper-T-width is constant, we introduce some applications of hyper-D-width and hyper-T-width in solving hard problems such as minimum vertex cover, minimum dominating set, and multicut
Signed graphs cospectral with the path
, Article Linear Algebra and Its Applications ; Volume 553 , 2018 , Pages 104-116 ; 00243795 (ISSN) ; Haemers, W. H ; Maimani, H. R ; Parsaei Majd, L ; Sharif University of Technology
Elsevier Inc
2018
Abstract
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
Orientations of graphs avoiding given lists on out-degrees
, Article Journal of Graph Theory ; Volume 93, Issue 4 , 2020 , Pages 483-502 ; Dalirrooyfard, M ; Ehsani, K ; Ozeki, K ; Sherkati, R ; Sharif University of Technology
Wiley-Liss Inc
2020
Abstract
Let G be a graph and F: V(G) → 2N be a mapping. The graph G is said to be F- avoiding if there exists an orientation O of G such that do +(v)∉ F (v) for every v ∈ V (G), where do +(v) denotes the out-degree of v in the directed graph G with respect to O. In this paper it is shown that if G is bipartite and |F (v)| ≤ dG (v)/2 for every v ∈ V (G), then G is F-avoiding. The bound |F (v)| ≤ dG (v)/2 is best possible. For every graph G, we conjecture that if |F (v)| ≤ 1/2 dG (v)-1) for every v ∈ V (G), then G is F-avoiding. We also argue about this conjecture for the best possibility of the conditions and also show some partial solutions. © 2019 Wiley Periodicals, Inc
Energy-landscape networks of spin glasses
, Article Physical Review E - Statistical, Nonlinear, and Soft Matter Physics ; Volume 77, Issue 3 , 2008 ; 15393755 (ISSN) ; Seyed Allaei, H ; Ejtehadi, M. R ; Sharif University of Technology
2008
Abstract
We have studied the topology of the energy landscape of a spin-glass model and the effect of frustration on it by looking at the connectivity and disconnectivity graphs of the inherent structure. The connectivity network shows the adjacency of energy minima whereas the disconnectivity network tells us about the heights of the energy barriers. Both graphs are constructed by the exact enumeration of a two-dimensional square lattice of a frustrated spin glass with nearest-neighbor interactions up to the size of 27 spins. The enumeration of the energy-landscape minima as well as the analytical mean-field approximation show that these minima have a Gaussian distribution, and the connectivity...
An enhanced random-walk method for content locating in P2P networks
, Article 27th International Conference on Distributed Computing Systems Workshops, ICDCSW'07, Toronto, ON, 22 June 2007 through 29 June 2007 ; 2007 ; 0769528384 (ISBN); 9780769528380 (ISBN) ; Firooz, M. H ; Pakravan, M. R ; Nasiri Avanaki, A ; Sharif University of Technology
2007
Abstract
The important problem of content location in an unstructured distributed network (such as P2P, with no central searching system, graph construction control or file placement regulation) is addressed. The existing methods that are based on either flooding or random walk impose a large traffic load on the network or require a long time to search. In this work, we propose a method that outperforms the existing methods in both of these measures. These advantages are achieved by publishing traces of the contents of each node in its nearby nodes, so that the closer nodes to the target have a stronger trace of it. Such traces are used to rapidly locate the desired content. The superb performance of...