TY - JOUR
T1 - α-labelings and the structure of trees with nonzero α-deficit
AU - Brinkmann, Gunnar
AU - Crevals, Simon
AU - Mélot, Hadrien
AU - Rylands, Leanne
AU - Steffen, Eckhard
PY - 2012
Y1 - 2012
N2 - We present theoretical and computational results on α-labelings of trees. The theorems proved in this paper were inspired by the results of a computer investigation of α-labelings of all trees with up to 26 vertices, all trees with maximum degree 3 and up to 36 vertices, all trees with maximum degree 4 and up to 32 vertices and all trees with maximum degree 5 and up to 31 vertices. We generalise a criterion for trees to have nonzero α-deficit, and prove an unexpected result on the α-deficit of trees with a vertex of large degree compared to the order of the tree.
AB - We present theoretical and computational results on α-labelings of trees. The theorems proved in this paper were inspired by the results of a computer investigation of α-labelings of all trees with up to 26 vertices, all trees with maximum degree 3 and up to 36 vertices, all trees with maximum degree 4 and up to 32 vertices and all trees with maximum degree 5 and up to 31 vertices. We generalise a criterion for trees to have nonzero α-deficit, and prove an unexpected result on the α-deficit of trees with a vertex of large degree compared to the order of the tree.
KW - Graceful Tree Conjecture
KW - graph labelings
KW - graph theory
KW - trees (mathematics)
UR - http://handle.uws.edu.au:8081/1959.7/517739
UR - http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/1833/3795
M3 - Article
SN - 1365-8050
VL - 14
SP - 159
EP - 174
JO - Discrete Mathematics and Theoretical Computer Science
JF - Discrete Mathematics and Theoretical Computer Science
IS - 1
ER -