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A Computational Approach to the Graceful Tree Conjecture
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A Computational Approach to the Graceful Tree Conjecture
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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.
Forward citations
Cited by 4 Pith papers
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Alternating Extremes in Graceful Labelings of Full Binary Trees and Spider Trees
Comb full binary trees and leaf-extended spiders built from self-matched legs admit the newly stated pinned-spine/graceful labelings, and the pinned-spine conjecture is verified computationally for all rooted FBTs thr...
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Graceful labelings of spiders with three-edge legs and pendant leaves at the center
Every spider tree with k three-edge legs and m pendant leaves at the center is graceful for all k ≥ 1 and m ≥ 0.
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Graceful labelings of spiders with three-edge legs and pendant leaves at the center
All spiders with k legs of length 3 and m pendant leaves at the center are graceful for every k ≥ 1 and m ≥ 0.
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Alternating Extremes in Graceful Labelings of Full Binary Trees and Spider Trees
Comb full binary trees admit pinned-spine graceful labelings with alternating extremes; self-matched spider legs pack into graceful spiders with leftover hub leaves.
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