Graceful Tree Labeling
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منابع مشابه
Constructing Graceful Graphs with Caterpillars
A graceful labeling of a graph G of size n is an injective assignment of integers from {0, 1,..., n} to the vertices of G, such that when each edge of G has assigned a weight, given by the absolute dierence of the labels of its end vertices, the set of weights is {1, 2,..., n}. If a graceful labeling f of a bipartite graph G assigns the smaller labels to one of the two stable sets of G, then f ...
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The Graceful Tree Conjecture claims that every finite simple tree of order n can be vertex labeled with integers {1, 2, ...n} so that the absolute values of the differences of the vertex labels of the end-vertices of edges are all distinct. That is, a graceful labeling of a tree is a vertex labeling f , a bijection f : V (Tn) −→ {1, 2, ...n}, that induces an edge labeling g(uv) = |f(u)− f(v)| t...
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One of the most famous open problems in graph theory is the Graceful Tree Conjecture, which states that every finite tree has a graceful labeling. In this paper, we define graceful labelings for countably infinite graphs, and state and verify a Graceful Tree Conjecture for countably infinite trees.
متن کاملModular 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 کاملEmbedding an Arbitrary Tree in a Graceful Tree
A function f is called a graceful labeling of a graph G with m edges if f is an injective function from V (G) to {0, 1, 2, · · · ,m} such that when every edge uv is assigned the edge label |f(u)− f(v)|, then the resulting edge labels are distinct. A graph which admits a graceful labeling is called a graceful graph. The popular Graceful Tree Conjecture states that every tree is graceful. The Gra...
متن کاملA substitution theorem for graceful trees and its applications
A graceful labeling of a graphG = (V,E) assigns |V | distinct integers from the set {0, . . . , |E|} to the vertices of G so that the absolute values of their differences on the |E| edges of G constitute the set {1, . . . , |E|}. A graph is graceful if it admits a graceful labeling. The forty-year old Graceful Tree Conjecture, due to Ringel and Kotzig, states that every tree is graceful. We pro...
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تاریخ انتشار 2008