Variable neighborhood search for extremal graphs: 1 The AutoGraphiX system
نویسندگان
چکیده
منابع مشابه
Variable neighborhood search for extremal vertices: The system AutoGraphiX-III
More than fifteen years after the beginning of the development of AutoGraphiX (AGX), a third version of the software is made available. Since the program was rewritten from scratch, it was the opportunity to look forward and consider new avenues. From the user’s point of view, the interface is completely changed, which allows the display of multiple information which was not possible in the pre...
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Usual graph classes, such as complete graphs, paths, cycles and stars, frequently appear as extremal graphs in graph theory problems. Here we want to turn the reader’s attention to two novel, simply defined, graph classes that appear as extremal graphs in several graph theory problems. We call them bags and bugs. As examples of problems where bags and bugs appear, we show that balanced bugs max...
متن کاملVariable Neighborhood Search for Extremal Graphs. 17. Further Conjectures and Results about the Index∗
The AutoGraphiX 2 system is used to compare the index of a connected graph G with a number of other graph theoretical invariants, i.e., chromatic number, maximum, minimum and average degree, diameter, radius, average distance, independence and domination numbers. In each case, best possible lower and upper bounds, in terms of the order of G, are sought for sums, differences, ratios and products...
متن کاملVariable neighborhood search for extremal graphs.17. Futher conjectures and results about the index
The AutoGraphiX 2 system is used to compare the index of a connected graph G with a number of other graph theoretical invariants, i.e., chromatic number, maximum, minimum and average degree, diameter, radius, average distance, independence and domination numbers. In each case, best possible lower and upper bounds, in terms of the order of G, are sought for sums, differences, ratios and products...
متن کاملVariable Neighborhood Search for Extremal Graphs, 24. Results about the clique number
A set of vertices S in a graph G is a clique if any two of its vertices are adjacent. The clique number ω is the maximum cardinality of a clique in G. A series of best possible lower and upper bounds on the difference, sum, ratio or product of ω and some other common invariants of G were obtained by the system AGX 2, and most of them proved either automatically or by hand. In the present paper,...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00206-x