Sharif Digital Repository

It is well known that all starlike trees, i.e. trees with exactly one vertex of degree at least three, are determined by their Laplacian spectrum. A double starlike tree is a tree with exactly two vertices of degree at least three. In 2009, the following question was posed: Are all the double starlike trees determined by their Laplacian spectra? In this direction, it was proved that one special double starlike tree Hn(p,p) is determined by its Laplacian spectrum, where Hn(p,q) is a tree obtained by joining p pendant vertices to an end vertex of a path of order and then joining pendant vertices to another end of the path. Also, the banana tree Bn,k is a tree obtained by joining a vertex to... 

A harmonious coloring of G is a proper vertex coloring of G such that every pair of colors appears on at most one pair of adjacent vertices. The harmonious chromatic number of G, h(G), is the minimum number of colors needed for a harmonious coloring of G. We show that if T is a forest of order n with maximum degree Δ(T)≥n+23, then h(T) = {Δ(T)+2,if T has non-adjacent vertices of degree Δ(T);Δ(T)+1,otherwise.Moreover, the proof yields a polynomial-time algorithm for an optimal harmonious coloring of such a forest  

Let G = {g1,...,gn} be a finite abelian group. Consider the complete graph with the vertex set {g1.....,.....g n}. The G-coloring of Kn is a proper edge coloring in which the color of edge {gi,gj} gi g i + gj, 1 ≤ i < 3 ≤ n. We prove that in the G-coloring of the complete graph Kn, there exists a multicolored Hamilton path if G is not an elementary abelian 2-group. Furthermore, we show that if n is odd, then the G-coloring of Kn can be decomposed into multicolored 2-factors and there are exactly lr/2 multicolored r-uniform 2-factors in this decomposition where lr is the number of elements of order r in G, 3 ≤ r ≤ n. This provides a generalization of a recent result due to Constantine which... 

Recently, tree structures have become a popular way for storing and manipulating huge amount of data. Classification of these data can facilitate storage, retrieval, indexing, query answering and different processing operations. In this paper, we present C-Classifier and M-Classifier algorithms for rule based classification of tree structured data. These algorithms are based on extracting especial tree patterns from training dataset. These tree patterns, i.e. closed tree patterns and maximal tree patterns are capable of extracting characteristics of training trees completely and non-redundantly. Our experiments show that M-Classifier significantly reduces running time and complexity. As... 

The novel generation of binary partition trees inside the wavelet domain is presented, where spatial frequency is used in conjunction with colour to produce a threshold free tree for segmentation. The method forces objects to reside inside single branches of the tree by constraining their development using multi-dimensional descriptors. © The Institution of Engineering and Technology 2007  

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... 

Liu and Xu (1998) and Ellingham, Nam and Voss (2002) independently showed that every k-edge-connected simple graph G has a spanning tree T such that for each vertex v, dT(v) ≤ ⌈ d(v)/k ⌉ + 2. In this paper we show that every k-edge-connected graph G has a spanning tree T such that for each vertex v, dT(v)≤ ⌈ d(v)-2/k ⌉ + 2; also if G has k edge-disjoint spanning trees, then T can be found such that for each vertex v, dT(v) ≤ ⌈ d(v)-1/k ⌉ + 1. This result implies that every (r-1)-edge-connected r-regular graph (with r ≥ 4) has a spanning Eulerian subgraph whose degrees lie in the set {2,4,6}; also reduces the edge-connectivity needed for some theorems due to Barát and Gerbner (2014) and... 

One of the main objectives of all watermarking algorithms is to provide a secure method for detecting all or part of the watermark pattern in case of usual attacks to a watermarked image. In this paper we introduce a method that is suitable for any spatial domain watermarking algorithms, such that, it can provide a measure for the level of robustness when a given watermark is supposed to be embedded in a known host image. In order to increase the robustness of the watermarked image, for a watermark of n bits, we embed it s times. Doing this, the entire image is divided into 16 equal size blocks. For each block the complexity of the sub-image in that block is measured. The number of... 

In this paper, Quad-Tree decomposition method is applied for areal upscaling of irregular shaped petroleum reservoirs. Quad-Tree decomposition is a recursive data structuring technique which generates an upscaled model with non-uniform (unstructured) gridblocks. This type of coarsening reduces the number of gridblocks, but preserves the main heterogeneity features of the original fine model. Because of the quadruplet nature of the Quad-Tree decomposition, this method cannot be used for upscaling of irregular-shaped models, directly. In this study, by circumscribing a square to the irregular-shaped reservoirs, a temporary model is obtained which can be upscaled by Quad-Tree decomposition.... 

A set S of vertices of a graph G = (V, E) is a dominating set if every vertex of V(G) S is adjacent to some vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set of G. The domination subdivision number sdγ(G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the domination number. Velammal in his Ph.D. thesis [Manonmaniam Sundaranar University, Tirunelveli, 1997] showed that for any tree T of order at least 3, 1 ≤ sdγ(T) ≤ 3. Furthermore, Aram, Favaron and Sheikholeslami, recently, in their paper entitled "Trees with domination subdivision number three," gave two characterizations of... 

Given a metric graph G, we are concerned with finding a spanning tree of G where the maximum weighted degree of its vertices is minimum. In a metric graph (or its spanning tree), the weighted degree of a vertex is defined as the sum of the weights of its incident edges. In this paper, we propose a 4.5-approximation algorithm for this problem. We also prove it is NP-hard to approximate this problem within a 2 - ε factor. © 2007 Elsevier B.V. All rights reserved  

A multicolored tree is a tree whose edges have different colors. Brualdi and Hollingsworth [5] proved in any proper edge coloring of the complete graph K2n(n > 2) with 2n -1 colors, there are two edge-disjoint multicolored spanning trees. In this paper we generalize this result showing that if (a1,..., ak) is a color distribution for the complete graph Kn, n ≥ 5, such that 2 ≤ a1 ≤ a2 ≤ ⋯ ≤ ak ≤ (n + 1)/2, then there exist two edge-disjoint multicolored spanning trees. Moreover, we prove that for any edge coloring of the complete graph Kn with the above distribution if T is a non-star multicolored spanning tree of Kn, then there exists a multicolored spanning tree T′ of Kn such that T and T′... 

In this paper, we show that by considering the factor of usage in instruction bundles in VLIW processors and using the slots filled with NOPs in bundles, we can improve the overall performance by reducing the total execution time of the program. By our proposed scheme, Combined Bundle Scheduling (CBS), we have gained better performance compared to that for the PDT scheme (Predicted Decision Tree scheduling) which is the best scheduling strategy known so far. © 2006 IEEE  

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  

Given a graph G with a set of terminals, two weight functions c and d defined on the edge set of G, and a bound D, a popular NP-hard problem in designing networks is to find the minimum cost Steiner tree (under function c) in G, to connect all terminals in such a way that its diameter (under function d) is bounded by D. Marathe et al. (J. Algoritm. 28(1), 142–171, 1998) proposed an (O(lnn),O(lnn)) approximation algorithm for this bicriteria problem, where n is the number of terminals. The first factor reflects the approximation ratio on the diameter bound D, and the second factor indicates the cost-approximation ratio. Later, Kapoor and Sarwat (Theory Comput. Syst. 41(4), 779–794, 2007)... 

In this paper, a diverse range of routing algorithms is classified into a new family of routings called zone-ordered label-based routing algorithms. The proposed classification is based on three common steps (factors) for generating such routings, namely, graph labeling, deadlock-free zones, and zone ordering. The main goal of this classification is to define several new routing concepts and streamline the knowledge on routing algorithms. Following the classification, a novel methodology is proposed to generate routing algorithms for irregular networks. The methodology uses the three mentioned steps to generate deadlock-free routings. Consequently, the methodology-based routings fall into... 

In this paper, a diverse range of routing algorithms is classified into a new family of routings called zone-ordered label-based routing algorithms. The proposed classification is based on three common steps (factors) for generating such routings, namely, graph labeling, deadlock-free zones, and zone ordering. The main goal of this classification is to define several new routing concepts and streamline the knowledge on routing algorithms. Following the classification, a novel methodology is proposed to generate routing algorithms for irregular networks. The methodology uses the three mentioned steps to generate deadlock-free routings. Consequently, the methodology-based routings fall into... 

Due to complicated implementation of IP multicast, application layer multicast has attracted the attention of researchers. Tree overlay has some challenges such as resiliency problems caused by peer churns and also network resources may not be efficiently used. Mesh overlay doesn't have such problems, but has a high delivery latency and overhead caused by pull mechanism. Using a hybrid mesh/tree overlay offers push pull approach and leads to use the advantages of both overlays simultaneously. Also in p2p networks a significant problem is heterogeneity of peers. In this paper we propose a hybrid mesh/tree overlay that by means of streaming layered coded video, addresses these challenges. This... 

The problem of finding nearest neighbors in a certain distance is well defined in machine learning area. There are well-known and exact solutions for it. However, in real world problems, especially in machine vision area, where we have a moving sensor and we want to know which objects of the scene are in the measurement range of it, two issues are important. First, usually in these problems, the time cost is more important than accuracy. It means they can tolerate some measurements error if they can do the process in real-time. Second, the location of an object can be described in the three-dimensional space and does not require the higher dimensions. According to these issues, we introduced...