In this paper we present and analyze new sequential and parallel heuristics to approximate the Minimum Linear Arrangement problem (MinLA). The heuristics consist in obtaining a first global solution using Spectral Sequencing and improving it locally through Simulated Annealing. In order to accelerate the annealing process, we present a special neighborhood distribution that tends to favor moves...

Graphs arise in numerous applications, such as the analysis of the Web, router networks, social networks, co-citation graphs, etc. Virtually all the popular methods for analyzing such graphs, for example, k-means clustering, METIS graph partitioning and SVD/PCA, require the user to specify various parameters such as the number of clusters, number of partitions and number of principal components...

The notion of an excellent quadratic form has been introduced by M. Knebusch 10, 11]. It has an obvious analogue for a semisimple linear algebraic group G over an arbitrary eld k: the group G is excellent if, for any eld extension K of k, the anisotropic kernel of the K-group G k K can be deened by a k-group. The aim of this paper is to investigate excellence properties of special linear and or...

Most of the traditional methods for shape classification are based on contour. They often encounter difficulties when dealing with classes that have large nonlinear variability, especially when the variability is structural or due to articulation. It is well-known that shape representation based on skeletons is superior to contour based representation in such situations. However, approaches to ...

the center (periphery) of a graph is the set of vertices with minimum (maximum)eccentricity. in this paper, the structure of centers and peripheries of some classes ofcomposite graphs are determined. the relations between eccentricity, radius and diameterof such composite graphs are also investigated. as an application we determinethe center and periphery of some chemical graphs such as nanotor...

we study the set of all determinants of adjacency matrices of graphs with a given number of vertices. using brendan mckay's data base of small graphs, determinants of graphs with at most $9$ vertices are computed so that the number of non-isomorphic graphs with given vertices whose determinants are all equal to a number is exhibited in a table. using an idea of m. newman, it is proved that if $...

mean labelings are a type of additive vertex labeling. this labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. in this paper we focus on mean labelings of some graphs that are the result of the corona operation. in parti...

the edge tenacity te(g) of a graph g is dened as:te(g) = min {[|x|+τ(g-x)]/[ω(g-x)-1]|x ⊆ e(g) and ω(g-x) > 1} where the minimum is taken over every edge-cutset x that separates g into ω(g - x) components, and by τ(g - x) we denote the order of a largest component of g. the objective of this paper is to determine this quantity for split graphs. let g = (z; i; e) be a noncomplete connected spli...

the energy of a graph is equal to the sum of the absolute values of its eigenvalues. two graphs of the same order are said to be equienergetic if their energies are equal. we point out the following two open problems for equienergetic graphs. (1) although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...

let $g=(v, e)$ be a graph. by emph{directional labeling (ord-labeling)} of an edge $x=uv$ of $g$ by an ordered $n$-tuple$(a_1,a_2,...,a_n)$, we mean a labeling of the edge $x$ such thatwe consider the label on $uv$ as $(a_1,a_2,...,a_n)$ in thedirection from $u$ to $v$, and the label on $x$ as$(a_{n},a_{n-1},...,a_1)$ in the direction from $v$ to $u$. inthis paper, we study graphs, called emph{...