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Document Type |
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Article In Journal |
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Document Title |
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Operator Decomposition of Graphs مشغل التحليل من الرسوم البيانية |
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Subject |
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Computer Science |
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Document Language |
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English |
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Abstract |
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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 join 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 Ï (P, Q), then G has the unique canonical (P, Q)-decomposition. |
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ISSN |
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1683-3198 |
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Journal Name |
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International Arab Journal of Information Technology |
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Volume |
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3 |
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Issue Number |
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2 |
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Publishing Year |
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1426 AH
2006 AD |
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Article Type |
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Article |
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Added Date |
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Saturday, February 5, 2011 |
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Researchers
| رزين قدوره | Quaddoura, Ruzayn | Researcher | Doctorate | rquaddoura@kau.edu.sa |
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Files
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28855.pdf
| pdf | Operator Decomposition of Graphs |
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