Sharif Digital Repository

Let X = fx1; : : : ; xng be the set of vertices of a hypergraph H and E = fe1; : : : ; emg be the set of its edges. The incidence matrix of hypergraph H is an n m and (0; 1)-matrix, N, such that nij = 1 if xi 2 ej and nij = 0, otherwise. A zero-sum flow for H is a vector with non-zero entries that is in the null space of N. A zero-sum k-flow is a flow with non-zero integer entries that absolue value of each entry is at
most k 1. In this thesis we study the existence of zero-sum flows for designs and hypergraphs. Also we consider zero-sum 3-flows in 2-Steiner designs  

In this thesis, we study some connections between the graph-theoretic and algebraic properties of co-maximal graph of algebraic structures. We follow two purposes. First, what properties of algebraic structures can be found from co-maximal graph of algebraic structures. Second, what geometric or graph theoretical properties of co-maximal graph of algebraic structures can be found from specefic algebraic structures. Let G be a group and I(G)∗be the set of all non-trivial sub-groups of G. The co-maximal graph of subgroups of G, denoted byΓ(G), is a graph with the vertex set I(G)∗and two distinct vertices H and K are adjacent if and only if HK=G. We char-acterize all groups whose co-maximal... 

Graph coloring is a fundamental problem in Computer Science. Despite its status as a computationally hard problem, it is still an active area of research. Depending on the specific area of requirement or an pplication, there are several variants of coloring.One such variant of graph coloring is Acyclic Graph Coloring. As with the case of proper coloring of graphs, Acyclic coloring can either be on vertex set or the edge set of a graph. When such a coloring is performed on the edges of a graph, it requires that after a graph has been colored there should not exist any cycle that runs on edges that are colored by only two colors. Such a cycle is called a bichromatic cycle. When a coloring does... 

Let G be a graph. A P3-factor of graph G is a subgraph of G such that each component is isomorphic to P3. In 1985 Akiyama and Kano conjectured that every 3-connected 3-regular graph of order divisible by 3 has a P3-factor. In this thesis we conjecture that every 3-connected 4-regular graph of order divisible by 3 has a P3-factor and also show that this conjecture concludes the previous one. Moreover, we investigate connected factors and some 3-vertex induced factors in graphs and show that every r-regular graph of order n (3 j n) has a P3-induced factor, if r _> 8n/ 9-1  

A signed graph is a graph with a sign attached to each edge. This article extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs.In particular, the largest Laplacian eigenvalue of a signed graph is investigated,which generalizes the corresponding results on the largest Laplacian eigenvalue of a graph.It is proved that (C2n+1; +) is uniquely determined by its Laplacian spectrum (or is DLS), where (C2n+1; +) is a signed cycle in which all edges have positive sign. On the other hand, we determine all Laplacian cospectral mates of (C2n; +) and hence (C2n; +) is not DLS. Also, we show that for every positive integer n, (Cn;) is DLS. Then, we study the spectrum of... 

A flow for a graph or a combinatorial design is an element of the nullspace of its incidence matrix. For an integer r ≥ 2, an r-flow is a flow whose values belong to {±1;±2; : : : ;±(r - 1)} and for a real number r ≥ 2, a circular r-flow is a flow whose values are real numbers in the set [-(r- 1),-1]U[1, r - 1].In the context of undirected graphs, flows are called zero-sum flows. In the first part of this dissertation, we study circular zero-sum flows of graphs and prove a necessary and sufficient condition for the existence of a circular zero-sum r-flow in a graph in terms of its factors. Also, we investigate the minimum value of r for which a k-regular graph has a circular r-flow and... 

The energy of a graph G, E(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. Gutman et al. proved that for every cubic graph of order n, E(G) ⩾ n. Here, we improve this result by showing that if G is a connected subcubic graph of order n, n ⩾ 8, then E(G) ⩾ 1.01n. Also, we prove that if G is a traceable subcubic graph of order n,then E(G) ⩾ 1.1n. Let G be a connected cubic graph of order n, it is shown that E(G) > n + 2, for n ⩾ 8 and we introduce an infinite family of connected cubic graphs whose for each element, say G, E(G) ⩾ 1.24n, and some important conjectures will be raised about this. At the end, for a graph G and its vertex induced subgraphs H and K,... 

Let G = (V(G),E(G)) be a Himple graph. An independent Het in a graph iH a et. of vert.iceH no t\vo of thE-'m are adjacE-'nt. The C'ardinality of a rnaxirnnrn independE-'ut fet in agraph G is r-ailed the independence number of G and is denoted b:y a:( G). The ndependencE- polynomial of G, I(G, :r), iH dE-'fined a l:ill'l I(G.1:) = ik(G)x'l \vhere iA.(G) is the number of iwh-•pendent ::->etH of G of Hize k and io(G) = 1. Then-' is nother graph polynomial \Vhir-h is called the domination poJ:ynomial and is defined as·ollmvs. A dominating sE-'t of G is a set 8 of vertices of G so that every vertex of G is fither in 5 or adjacent to a vertex in S. The domination... 

A signed graph is a pair like (G; ), where G is the underlying graph and : E(G) ! f1; +1g is a sign function on the edges of G. Here, we study the spectral determination problem for signed n-cycles (Cn; ) with respect to the adjacency spectrum and the Laplacian spectrum. In particular we prove that signed odd cycles and unbalanced even cycles are uniquely determined by their Laplacian spectrums, but balanced even cycles are not, and we find all L-cospectral mates for them. Moreover, signed odd cycles are uniquely determined by their spectrums but the signed even cycles, (except (C4;) and (C4; +)), are not and we find almost all cospectral mates for them. A mixed graph is obtained from a... 

Nowadays, microgyroscopes are among the most important products of MEMS. The production of small, precise and inexpensive gyroscopes has become possible as the result of recent developments in fabrication technology. In this thesis it is intended to introduce a new method for manufacturing more precise microgyroscopes regarding manufacture facilities. Using this new method, sensitivity and resistance of microgyroscopes are increased against noises which are primarily caused by vibration and rotation about undesirable axes. The rotational movement imposed on the gyro is detected through fluid flow within its torus channel. This transformation facilitates the measurement of the initial motion.... 

The fiber-reinforced composite materials possess advantage for structural purpose in various industries. Delamination is recognized as one of the major causes of damage during drilling of fiber reinforced composites, which not only reduces the structural integrity, but also has the potential for long-term performance deterioration. It is difficult to produce precise quality holes with high efficiency by conventional drilling method. Drilling is frequently applied in production cycle while the anisotropy and nonhomogeneity of composite materials affect the chip deformation and machining behavior during drilling. In this thesis, a new non-traditional drilling technology is presented for solve... 

Let G be a graph with adjacency matrix A and Δ be a diagonal matrix whose diagonal entries are the degree sequence of G. Then the matrices L = Δ− A and Q = Δ+A are called Laplacian matrix and signless Laplacian matrix of G, respectively. The eigenvalues of A, L, and Q are arranged decreasingly and denoted by λ1 ≥ · · · ≥ λn, μ1 ≥ · · · ≥ μn ≥ 0, and q1 ≥ · · · ≥ qn ≥ 0, respectively. The energy of a graph G is defined as E(G) :=
n
i=1
|λi|.
Furthermore, the incidence energy, the signed incidence energy, and the H¨uckel energy of G are
defined as
IE(G) :=
n
i=1
√
qi, LE(G) :=
n
i=1
√
μi, HE(G) :=

2
r
i=1 λi, n=... 

Internet video networks have already attracted millions of Internet users, and Internet video is one of the fast growing Internet services. The peer-to-peer (P2P) network is an efficient solution to supporting large scale video streaming on the Internet. P2P networks can deliver live multimedia content to millions of users with low cost at any time, and at anywhere they want. In this thesis, we investigate solutions to enhancing the performance of the unstructured mesh-based. Locality awareness or network proximity is one of the essential characteristics of P2P networks. In live P2P video streaming we face to some challenges like bandwidth heterogeneity of peers, and peer churn. In the P2P...