Modular gracious labellings of trees

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Modular gracious labellings of trees

A gracious labelling g of a tree is a graceful labelling in which, treating the tree as a bipartite graph, the label of any edge (d,u) (d a ‘down’ and u an ‘up’ vertex) is g(u) – g(d). A gracious k-labelling is one such that each residue class modulo k has the ‘correct’ numbers of vertex and edge labels that is, the numbers that arise by interpreting the labels of a gracious labelling modulo k....

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Connections between labellings of trees

There are many long-standing conjectures related with some labellings of trees. It is important to connect labellings that are related with conjectures. We find some connections between known labellings of simple graphs.

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Relaxed 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...

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connections between labellings of trees

there are many long-standing conjectures related with some labellings of trees. it is important to connect labellings that are related with conjectures. we find some connections between known labellings of simple graphs.

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Constructing Trees with Graceful Labellings Using Caterpillars

Hrnciar and Haviar [3] gave a method to a construct a graceful labeling for all trees of diameter at most five. Based on their method and the methods described in Balbuena et al [1], we shall describe a new construction for gracefully labeled trees by attaching trees to the vertices of a tree admitting a bipartite graceful labeling.

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2001

ISSN: 0012-365X

DOI: 10.1016/s0012-365x(00)00318-6