Graceful Tree Conjecture for Infinite Trees
نویسندگان
چکیده
منابع مشابه
Graceful Tree Conjecture for Infinite Trees
One of the most famous open problems in graph theory is the Graceful Tree Conjecture, which states that every finite tree has a graceful labeling. In this paper, we define graceful labelings for countably infinite graphs, and state and verify a Graceful Tree Conjecture for countably infinite trees.
متن کاملTowards the Graceful Tree Conjecture: A Survey
A graceful labelling of an undirected graph G with n edges is a one-to-one function from the set of vertices of G to the set {0, 1, 2, . . . , n} such that the induced edge labels are all distinct. An induced edge label is the absolute value of the difference between the two end-vertex labels. The Graceful Tree Conjecture states that all trees have a graceful labelling. In this survey we presen...
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Graceful tree conjecture is a well-known open problem in graph theory. Here we present a computational approach to this conjecture. An algorithm for finding graceful labelling for trees is proposed. With this algorithm, we show that every tree with at most 35 vertices allows a graceful labelling, hence we verify that the graceful tree conjecture is correct for trees with at most 35 vertices.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2009
ISSN: 1077-8926
DOI: 10.37236/154