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On loops, dominators, and dominance frontier

Proceedings of the ACM SIGPLAN 2000 conference on Programming language design and implementation, 2000
This article explores the concept of loops and loop nesting forests of control-flow graphs, using the problem of constructing the dominator tree of a graph and the problem of computing the iterated dominance frontier of a set of vertices in a graph as guiding applications. The contributions of this article include: (1) An axiomatic characterization, as
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On the Domination Integrity

International Journal of Foundations of Computer Science, 2019
The domination integrity of graph G is defined by [Formula: see text] where [Formula: see text] denotes the order of the largest component in [Formula: see text]. This parameter is a measures of vulnerability of a graph. In this paper, we determine the domination integrity of middle graph of graph [Formula: see text], graph [Formula: see text] and ...
Hüseyin Tokat, Alpay Kirlangiç
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Generalized dominators and post-dominators

Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '92, 1992
The notion of dominators is generalized to include multiple-vertex dominators in addition to single-vertex dominators. A multiple-vertex dominator of a vertex is a group of vertices that collectively dominate the vertex. Existing algorithms compute immediate single-vertex dominators, and an algorithm for computing immediate multiple-vertex dominators ...
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