منابع مشابه
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...
متن کاملConstructing 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.
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...
متن کاملConnections 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.
متن کاملImproper Graceful and Odd-graceful Labellings of Graph Theory
Abstract In this paper we define some new labellings for trees, called the in-improper and out-improper odd-graceful labellings such that some trees labelled with the new labellings can induce graceful graphs having at least a cycle. We, next, apply the new labellings to construct large scale of graphs having improper graceful/odd-graceful labellings or having graceful/odd-graceful labellings.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2002
ISSN: 1077-8926
DOI: 10.37236/1621