Authors: Cvetković, Dragoš
Davidović, Tatjana 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Multiprocessor interconnection networks with small tightness
Journal: International Journal of Foundations of Computer Science
Volume: 20
Issue: 5
First page: 941
Last page: 963
Issue Date: 1-Oct-2009
Rank: M23
ISSN: 0129-0541
DOI: 10.1142/S0129054109006978
Homogeneous multiprocessor systems are usually modelled by undirected graphs. Vertices of these graphs represent the processors, while edges denote the connection links between adjacent processors. Let G be a graph with diameter D, maximum vertex degree , the largest eigenvalue λ1 and m distinct eigenvalues. The products m and (D+1)λ1 are called the tightness of G of the first and second type, respectively. In recent literature it was suggested that graphs with a small tightness of the first type are good models for the multiprocessor interconnection networks. In a previous paper we studied these and some other types of tightness and some related graph invariants and demonstrated their usefulness in the analysis of multiprocessor interconnection networks. We proved that the number of connected graphs with a bounded tightness is finite. In this paper we determine explicitly graphs with tightness values not exceeding 9. There are 69 such graphs and they contain up to 10 vertices. In addition we identify graphs with minimal tightness values when the number of vertices is n = 2,..., 10.
Keywords: Graph Invariants | Interconnection Topologies | Multiprocessor Systems | Spectra of Graphs
Publisher: World Scientific

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