Results 31 to 40 of about 60,649 (158)
Propagating Graceful Graphs and Trees [PDF]
arXiv, 2021 In an attempt to prove the Graceful Tree Conjecture, we present two propagation of graphs. The first is to propagate graceful graphs, and the second is to propagate trees from a gracefully labeled tree. The motivation in propagating such graphs is to see how graphs behave in the lens of their adjacency matrices.
arxiv
A Graceful Algebraic Function Labelling of Rooted Symmetric Trees [PDF]
arXiv, 2021 Let T=(V,E) be a tree with vertex set V and edge set E. A graceful labelling f of T is an injective function f from V into {0, 1, ..., |E|} such that if edge uv is assigned the label g(uv)=|f(u)-f(v)| then the function g from E into {1, ..., |E|} is also injective (that is all edge labels are distinct).
arxiv
arXiv, 2020 A graceful labeling of a graph $G$ with $m$ edges consists of labeling the vertices of $G$ with distinct integers from $0$ to $m$ such that, when each edge is assigned as induced label the absolute difference of the labels of its endpoints, all induced edge labels are distinct.
arxiv
Lucas Graceful Labeling For Some Graphs [PDF]
viXra, 2011 By a graph, we mean a finite undirected graph without loops or multiple edges.
A. Nagarajan +2 more
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On graceful labelings of trees
, 2018 We prove via a composition lemma, the Kotzig-Ringel-Rosa conjecture, better known as the Graceful Labeling Conjecture. We also prove via a stronger version of the composition lemma a stronger form of the Graceful Labeling Conjecture.
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On super edge-graceful trees of diameter four [PDF]
arXiv, 2011 In "On the super edge graceful trees of even orders," Chung, Lee, Gao, and Schaffer posed the following problem: Characterize trees of diameter 4 which are super edge-graceful. In this paper, we provide super edge-graceful labelings for all caterpillars and even size lobsters of diameter 4 which permit such labelings.
arxiv
A Computational Approach to the Graceful Tree Conjecture [PDF]
arXiv, 2010 Graceful tree conjecture is a well-known open problem in graph theory. Here we present a computational approach to this conjecture. An algorithm for finding graceful labelling for trees is proposed. With this algorithm, we show that every tree with at most 35 vertices allows a graceful labelling, hence we verify that the graceful tree conjecture is ...
arxiv
Arithmetic Sequential Graceful Labeling on Star Related Graphs [PDF]
, 2022 P Sumathi, G Geetha Ramani
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One curious identity counting graceful labelings
Enumerative Combinatorics and Applications, 2021 Let $a$ and $b$ be positive integers with prime factorisations $a = p_1^np_2^n$ and $b = q_1^nq_2^n$. We prove that the number of essentially distinct $α$-graceful labelings of the complete bipartite graph $K_{a, b}$ equals the alternating sum of fourth powers of binomial coefficients $(-1)^n[\binom{2n}{0}^4 - \binom{2n}{1}^4 + \binom{2n}{2}^4 - \binom{
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