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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.
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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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