Sharif Digital Repository

In this paper, we envision a solution to the problem of capturing an intruder in a product network. This solution is derived based on the assumed existing algorithms for basic member graphs of a graph product. In this problem, a team of cleaner agents are responsible for capturing a hostile intruder in the network. While the agents can move in the network one hop at a time, the intruder is assumed to be arbitrarily fast in a way that it can traverse any number of nodes contiguously as far as no agents reside in those nodes. Here, we consider a version of the problem where each agent can replicate new agents. Hence, the algorithm start with a single agent and new agents are created on demand.... 

Some new relations have been established between Wiener indices, stability numbers and clique numbers for several classes of composite graphs that arise via graph products. For three of considered operations we show that they make a multiplicative pair with the clique number  

In this article, we introduce the algebra of block-symmetric cylinders and we show that symmetric cylindrical constructions on base-graphs admitting commutative decompositions behave as generalized tensor products. We compute the characteristic polynomial of such symmetric cylindrical constructions in terms of the spectra of the base-graph and the cylinders in a general setting. This gives rise to a simultaneous generalization of some well-known results on the spectra of a variety of graph amalgams, as various graph products, graph subdivisions and generalized Petersen graph constructions. While our main result introduces a connection between spectral graph theory and commutative... 

In this paper, a new graph product, called Edge Graph Product (EGP) is proposed by replacing each edge in the multiplicand graph by a copy of the multiplier graph via two candidate nodes. The edge product, unlike other products already proposed, results in a graph whose number of edges is numerical product of the number of the edges in the multiplicand and multiplier graphs, and the number of vertices is not equal to the numerical product of the number of vertices in the multiplicand and multiplier graphs. After formal definition of the new product, some basic properties of the product operator are studied. We then address Hamiltonian, Eulerian and routing properties of the new product, and... 

The minimum number of complete bipartite subgraphs needed to partition the edges of a graph G is denoted by b (G). A known lower bound on b (G) states that b (G) ≥max {p (G), q (G)}, where p (G) and q (G) are the numbers of positive and negative eigenvalues of the adjacency matrix of G, respectively. When equality is attained, G is said to be eigensharp and when b (G) = max {p (G), q (G)} + 1, G is called an almost eigensharp graph. In this paper, we investigate the eigensharpness of graphs with at most one cycle and products of some families of graphs. Among the other results, we show that Pm ∨ Pn, Cm ∨ Pn for m ≡ 2, 3 (mod 4) and Qn when n is odd are eigensharp. We obtain some results on... 

In this paper, we propose the first comprehensive mathematical performance model for product networks where fully adaptive routing is applied. Besides the generality of this model which makes it suitable to be used for any product graph, our analysis shows that the proposed model exhibits high accuracy. Simulation results show the validity and accuracy of the model even in heavy traffic and saturation region, where other models have severe problems for prediction. © 2007 IEEE  

In a large system, it is neither economical nor efficient to equip each node with a copy of the resource, and it is desirable to distribute the copies of the resource so that certain performance measure is obtained. In this paper we consider the problem of distributing resources in the edge product of networks. The algorithms presented in this paper make use of the known placements for the basic graphs composing the product graph. Therefore, in these placements we avoid the additional costs needed for deploying and rescaling the network. © 2008 IEEE