Journal ArticleDOI
Circulants and their connectivities
Frank Boesch,Ralph Tindell +1 more
TLDR
A new result is presented which answers the previously unsolved question of characterizing the connection sequence of circulants having point connectivity equal to point degree and develops some theorems regarding a new generalization of connectivity known as super-connectivity.Abstract:
There is diverse literature on various properties of a class of graphs known as circulants. We present a new result which answers the previously unsolved question of characterizing the connection sequence of circulants having point connectivity equal to point degree. We also develop some theorems regarding a new generalization of connectivity known as super-connectivity. In addition, we give a survey of published results pertinent to the study of connectivity of circulants.read more
Citations
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Book
Evolution of Parallel Cellular Machines: The Cellular Programming Approach
TL;DR: Universal computation in quasi-uniform cellular automata and coevolving architectures for cellular machines are studied.
Journal ArticleDOI
On the extraconnectivity of graphs
J. Fàbrega,Miguel Angel Fiol +1 more
TL;DR: Substantial conditions are given, relating the diameter of G with its girth, to assure optimum values of these conditional connectivities of G.
Book ChapterDOI
Cayley graphs and interconnection networks
TL;DR: This work first surveys some classes of Cayley graphs which are well studied as models of interconnection networks, with emphasis on loads of nodes and links in routings.
BookDOI
Evolution of Parallel Cellular Machines
TL;DR: This volume presents a number of systems, which are essentially generalizations of the well-known cellular automata (CA) model, which present an excellent point of departure for forays into parallel cellular machines.
Journal ArticleDOI
An adaptive least squares algorithm for the efficient training of artificial neural networks
TL;DR: In this paper, a novel learning algorithm is developed for the training of multilayer feedforward neural networks, based on a modification of the Marquardt-Levenberg least-squares optimization method.
References
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Book
Graph theory with applications
TL;DR: In this paper, the authors present Graph Theory with Applications: Graph theory with applications, a collection of applications of graph theory in the field of Operational Research and Management. Journal of the Operational research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.
Journal ArticleDOI
Graph theory with applications (revised edition), by J. A. Bondy and U.S.R. Murty. Pp x, 264. £5·95 paperback. 1977. SBN 0 333 22694 1 (Macmillan)
Journal ArticleDOI
The maximum connectivity of a graph.
TL;DR: The maximum diameter, and the minimum diameter are obtained and two unsolved problems concerning the distribution of the values of the connectivity and the diameter are included.
Journal ArticleDOI
Graphs with circulant adjacency matrices
Bernard Elspas,James Turner +1 more
TL;DR: In this paper, the connection set determined by the first row of a circulant adjacency matrix is shown to not be multiplicatively related to the connected set of an isomorphic graph.
Journal ArticleDOI
Connectivity of transitive graphs
TL;DR: In this paper, the conditions imposed by edge-transitivity and vertextransitivity on the connectivity of simple graphs are investigated and a special attention is given to the structure of those vertex-transitive graphs for which the degree of regularity exceeds the connectivity.