Results 21 to 30 of about 848 (243)
Discrete Mathematics, 1991 Using the concept of a Skolem sequence \(\{u_ 1,\ldots,u_{2n}\}\) of \(2n\geq 2\) terms, \(u_ i\in\mathbb{N}\), the authors introduce a new kind of vertex labeling of a graph \(G=(V,E)\) arising from the well-known concept of the graceful labeling of \(G\) by substituting the graceful (injective) mapping \(f:V\to\{0,1,\ldots,| E|\}\) by \(f:V\to\{1,2 ...
Lee, S.M., Shee, S.C.
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Dividing Graceful Labeling of Certain Tree Graphs
Tikrit Journal of Pure Science, 2020 A tree is a connected acyclic graph on n vertices and m edges. graceful labeling of a tree defined as a simple undirected graph G(V,E) with order n and size m, if there exist an injective mapping that induces a bijective mapping defined by for ...
Abdullah Zahraa O +2 more
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The Gracefulness of the Join of Graphs
Electronic Notes in Discrete Mathematics, 2015 Abstract We give a brief survey on the gracefulness of the join of two graphs, and present results on the gracefulness of the join of a cycle and a broken path.
Khee Meng Koh, L. Y. Phoon, Kian Wee Soh
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Graceful labeling construction for some special tree graph using adjacency matrix
Electronic Journal of Graph Theory and Applications, 2023 In 1967, Rosa introduced β − labeling which was then popularized by Golomb under the name graceful. Graceful labeling on a graph G is an injective function f : V(G)→{0, 1, 2, …, |E(G)|} such that, when each edge uv ∈ E(G) is assigned the label |f(u)−f(v)|
Nikson Simarmata +2 more
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Radio Heronian Mean k-Graceful Labeling on Degree Splitting of Graphs
Ratio Mathematica, 2023 A mapping g:V\left(G\right)\rightarrow{k,k+1,\ldots,k+N-1} is a radio heronian mean k-labeling such that if for any two distinct vertices s and t of G, d\left(s,t\right)+\left\lceil\frac{g\left(s\right)+g\left(t\right)+\sqrt{g\left(s\right)g\left(t\right)
K Sunitha, K Vimal Rani
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Further results on super graceful labeling of graphs
AKCE International Journal of Graphs and Combinatorics, 2016 Let G=(V(G),E(G)) be a simple, finite and undirected graph of order p and size q. A bijection f:V(G)∪E(G)→{k,k+1,k+2,…,k+p+q−1} such that f(uv)=|f(u)−f(v)| for every edge uv∈E(G) is said to be a k-super graceful labeling of G.
Gee-Choon Lau, Wai Chee Shiu, Ho-Kuen Ng
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AKCE International Journal of Graphs and Combinatorics, 2021 We introduce new labeling called m-bonacci graceful labeling. A graph G on n edges is m-bonacci graceful if the vertices can be labeled with distinct integers from the set such that the derived edge labels are the first n m-bonacci numbers.
Kalpana Mahalingam +1 more
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Graceful Labeling For bipartite graceful Graphs and related Graphs
, 2020 The concept of graceful labels was proposed by Rosa, scholars began to study graceful labels of various graphs and obtained relevant results.Let the graph is a bipartite graceful graph, we have proved some graphs are graceful labeling in this paper.
Liu, Chunfeng +2 more
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Radio Number of Hamming Graphs of Diameter 3
Theory and Applications of Graphs, 2022 For $G$ a simple, connected graph, a vertex labeling $f:V(G)\to \Z_+$ is called a \emph{radio labeling of $G$} if it satisfies $|f(u)-f(v)|\geq\diam(G)+1-d(u,v)$ for all distinct vertices $u,v\in V(G)$.
Jason DeVito +2 more
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The subdivision graph of a graceful tree is a graceful tree
Discrete Mathematics, 1998 A graph \(G= (V,E)\) is graceful, if there is a numbering \(f\) of the vertices from \(1\) to \(| V|\), such that all values \(| f(v)- f(w)|\) are distinct for all edges \(\{v,w\}\in E\). The subdivision graph of a graph is obtained by adding a vertex on the middle of each edge. It is shown that the subdivision graph of a graceful tree is also graceful.
M. Burzio, G. Ferrarese
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