On α-labellings of lobsters and trees with a perfect matching

A graceful labelling of a tree T is an injective function f:V(T)→{0,…,|E(T)|} such that {|f(u)−f(v)|:uv∈E(T)}={1,…,|E(T)|}. An α-labelling of a tree T is a graceful labelling f with the additional property that there exists an integer k∈{0,…,|E(T)|} such that, for each edge uv∈E(T), either f(u)≤k...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2019-09, Vol.268, p.137-151
Main Authors: Luiz, Atílio G., Campos, C.N., Richter, R. Bruce
Format: Article
Language:English
Subjects:
[formula omitted]-labelling
Graceful labelling
Graceful tree conjecture
Labeling
Lobsters
Matching
Maximum degree three
Trees
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Summary:A graceful labelling of a tree T is an injective function f:V(T)→{0,…,|E(T)|} such that {|f(u)−f(v)|:uv∈E(T)}={1,…,|E(T)|}. An α-labelling of a tree T is a graceful labelling f with the additional property that there exists an integer k∈{0,…,|E(T)|} such that, for each edge uv∈E(T), either f(u)≤k
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2019.05.004