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Operator decomposition of graphs
Author
Source
The International Arab Journal of Information Technology
Issue
Vol. 3, Issue 2 (30 Apr. 2006), pp.152-164, 13 p.
Publisher
Publication Date
2006-04-30
Country of Publication
Jordan
No. of Pages
13
Main Subjects
Information Technology and Computer Science
Abstract EN
In this paper we introduce a new form of decomposition of graphs, the (P, Q)-decomposition.
We first give an optimal algorithm for finding the 1-decomposition of a graph which is a special case of the (P, Q)-decomposition which was first introduced in [21].
We then examine the connections between the 1-decomposition and well known forms of decomposition of graphs, namely, modular and homogeneous decomposition.
The characterization of graphs totally decomposable by 1-decomposition is also given.
The last part of our paper is devoted to a generalization of the 1- decomposition.
We first show that some basic properties of modular decomposition can be extended in a new form of decomposition of graphs that we called operator decomposition.
We introduce the notion of a (P, Q)-module, where P and Q are hereditary graph-theoretic properties, the notion of a (P, Q)-split graph and the closed hereditary class (P, Q) of graphs (P and Q are closed under the operations of john of graphs and disjoint union of graphs, respectively).
On this base, we construct a special case of the operator decomposition that is called (P, Q)-decomposition.
Such decomposition is uniquely determined by an arbitrary minimal nontrivial (P, Q)-module in G.
In particular, if G ∉ (P, Q), then G has the unique canonical (P, Q)-decomposition.
American Psychological Association (APA)
Quaddoura, Ruzayn. 2006. Operator decomposition of graphs. The International Arab Journal of Information Technology،Vol. 3, no. 2, pp.152-164.
https://search.emarefa.net/detail/BIM-11810
Modern Language Association (MLA)
Quaddoura, Ruzayn. Operator decomposition of graphs. The International Arab Journal of Information Technology Vol. 3, no. 2 (Apr. 2006), pp.152-164.
https://search.emarefa.net/detail/BIM-11810
American Medical Association (AMA)
Quaddoura, Ruzayn. Operator decomposition of graphs. The International Arab Journal of Information Technology. 2006. Vol. 3, no. 2, pp.152-164.
https://search.emarefa.net/detail/BIM-11810
Data Type
Journal Articles
Language
English
Notes
includes bibliographical references : p. 164
Record ID
BIM-11810