Abstract: An algebraic framework for processing graph signals
axiomatically designates the graph adjacency matrix as the shift
operator. In this setup, we often encounter a problem wherein we
know the filtered output and the filter coefficients, and need to
find out the input graph signal. Solution to this problem using
direct approach requires O(N3) operations, where N is the number
of vertices in graph. In this paper, we adapt the spectral graph
partitioning method for partitioning of graphs and use it to reduce
the computational cost of the filtering problem. We use the example
of denoising of the temperature data to illustrate the efficacy of the
approach.
Abstract: In this paper a deterministic polynomial-time
algorithm is presented for the Clique problem. The case is considered
as the problem of omitting the minimum number of vertices from the
input graph so that none of the zeroes on the graph-s adjacency
matrix (except the main diagonal entries) would remain on the
adjacency matrix of the resulting subgraph. The existence of a
deterministic polynomial-time algorithm for the Clique problem, as
an NP-complete problem will prove the equality of P and NP
complexity classes.
Abstract: Let G be a graph of order n. The second stage adjacency matrix of G is the symmetric n × n matrix for which the ijth entry is 1 if the vertices vi and vj are of distance two; otherwise 0. The sum of the absolute values of this second stage adjacency matrix is called the second stage energy of G. In this paper we investigate a few properties and determine some upper bounds for the largest eigenvalue.
Abstract: In this paper, we represent protein structure by using
graph. A protein structure database will become a graph database.
Each graph is represented by a spectral vector. We use Jacobi
rotation algorithm to calculate the eigenvalues of the normalized
Laplacian representation of adjacency matrix of graph. To measure
the similarity between two graphs, we calculate the Euclidean
distance between two graph spectral vectors. To cluster the graphs,
we use M-tree with the Euclidean distance to cluster spectral vectors.
Besides, M-tree can be used for graph searching in graph database.
Our proposal method was tested with graph database of 100 graphs
representing 100 protein structures downloaded from Protein Data
Bank (PDB) and we compare the result with the SCOP hierarchical
structure.
Abstract: This paper simulates the ad-hoc mesh network in rural areas, where such networks receive great attention due to their cost, since installing the infrastructure for regular networks in these areas is not possible due to the high cost. The distance between the communicating nodes is the most obstacles that the ad-hoc mesh network will face. For example, in Terranet technology, two nodes can communicate if they are only one kilometer far from each other. However, if the distance between them is more than one kilometer, then each node in the ad-hoc mesh networks has to act as a router that forwards the data it receives to other nodes. In this paper, we try to find the critical number of nodes which makes the network fully connected in a particular area, and then propose a method to enhance the intermediate node to accept to be a router to forward the data from the sender to the receiver. Much work was done on technological changes on peer to peer networks, but the focus of this paper will be on another feature which is to find the minimum number of nodes needed for a particular area to be fully connected and then to enhance the users to switch on their phones and accept to work as a router for other nodes. Our method raises the successful calls to 81.5% out of 100% attempt calls.
Abstract: In this paper a new definition of adjacency matrix in
the simple graphs is presented that is called fuzzy adjacency matrix,
so that elements of it are in the form of 0 and
n N
n
1 , ∈
that are
in the interval [0, 1], and then some charactristics of this matrix are
presented with the related examples . This form matrix has complete
of information of a graph.