منابع مشابه
Modular Edge-Graceful Trees
Ryan Jones, Western Michigan University We introduce a modular edge-graceful labeling of a graph a dual concept to the common graceful labeling. A 1991 conjecture known as the Modular Edge-Graceful Tree Conjecture states that every tree of order n where n 6≡ 2 (mod 4) is modular edge-graceful. We show that this conjecture is true. More general results and questions on this topic are presented.
متن کاملA Survey of Graceful Trees
A tree of order n is said to be graceful if the vertices can be assigned the labels {0, . . . , n−1} such that the absolute value of the differences in vertex labels between adjacent vertices generate the set {1, . . . , n− 1}. The Graceful Tree Conjecture is the unproven claim that all trees are graceful. We present major results known on graceful trees from those dating from the problem’s ori...
متن کاملRelaxed Graceful Labellings of Trees
A graph G on m edges is considered graceful if there is a labelling f of the vertices of G with distinct integers in the set {0, 1, . . . ,m} such that the induced edge labelling g defined by g(uv) = |f(u) − f(v)| is a bijection to {1, . . . ,m}. We here consider some relaxations of these conditions as applied to tree labellings: 1. Edge-relaxed graceful labellings, in which repeated edge label...
متن کاملAn Extensive Survey of Graceful Trees
A tree with n vertices is called graceful if there exists a labeling of its vertices with the numbers from 1 to n such that the set of absolute values of the differences of the numbers assigned to the ends of each edge is the set {1, 2, .., n− 1}. The problem of whether or not all trees are graceful is still open. In this paper, we give an extensive survey of most of the results related to this...
متن کاملGraceful and harmonious labellings of trees
We establish that all trees on at most 27 vertices admit graceful labellings and all trees on at most 26 vertices admit harmonious labellings. A graceful labelling of a graph G with q edges is an injection f : V (G) → {0, 1, 2, . . . , q} such that when each edge xy ∈ E(G) is assigned the label, |f(x) − f(y)|, all of the edge labels are distinct. A graph which admits a graceful labelling is sai...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1980
ISSN: 0012-365X
DOI: 10.1016/0012-365x(80)90139-9