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Edge δ− Graceful Labeling for Some Cyclic-Related Graphs
Advances in Mathematical Physics, 2020 In this paper, we introduce a new type of labeling of a graph G with p vertices and q edges called edge δ− graceful labeling, for any positive integer δ, as a bijective mapping f of the edge set EG into the set δ,2δ,3δ,⋯,qδ such that the induced mapping ...
Mohamed R. Zeen El Deen
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LOCKS AND FORBIDDEN CONFIGURATIONS IN 4-GRACEFUL TREES
Ural Mathematical JournalLet \(f\) be a proper coloring of the vertices of a simple graph \(G\) into colors from the set of colors \(\{1, 2, \dots, k\}\). A coloring \(f\) on the set of edges of a graph \(G\) induces a function \(f'(e) = \vert{}f(u) - f(v)\vert{}\), where \(e ...
Vitaly A. Baransky +2 more
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Theory and Applications of Graphs, 2020 In his classical paper [14], Rosa introduced a hierarchical series of labelings called ρ, σ, β and α labeling as a tool to settle Ringel’s Conjecture which states that if T is any tree with m edges then the complete graph K2m+1 can be decomposed into 2m +
G. Sethuraman, M. Sujasree
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Computer search for graceful labeling: a survey
Electronic Journal of Graph Theory and Applications, 2022 This paper surveys the main computer search results for finding graceful labeling of trees. The paper is devoted to the memory of Mirka Miller, who made an outstanding contribution to the area of graph labeling.
Ljiljana Brankovic, Michael J. Reynolds
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Characterizations of kites as graceful graphs
CuboWe introduce and study an infinite family of graceful graphs, which we call kites. The kites are graphs where a path is joined with a graph "forming" a kite.
Miroslav Haviar, Katarina Kotuľová
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Edge even graceful labelling of some book graphs
Journal of Taibah University for Science, 2018 Elsonbaty and Daoud introduced a new type of labelling of a graph G with p vertices and q edges called an edge even graceful labelling if there is a bijection f from the edges of the graph to the set $\{2, 4,\ldots , 2q\}$ such that, when each vertex is ...
S.N. Daoud, Ahmed N. Elsawy
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Edge Odd Graceful Labeling of Cylinder and Torus Grid Graphs
IEEE Access, 2019 Solairaju and Chithra introduced a new type of labeling of a graph G with p vertices and q edges called an edge odd graceful labeling if there is a bijection f from the edges of the graph to the set {1, 3, ...
S. N. Daoud
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On graceful colorings of trees [PDF]
Mathematica Bohemica, 2017 A proper coloring $c V(G)\to\{1, 2,\ldots, k\}$, $k\ge2$ of a graph $G$ is called a graceful $k$-coloring if the induced edge coloring $c' E(G) \to\{1, 2, \ldots, k-1\}$ defined by $c'(uv)=|c(u)-c(v)|$ for each edge $uv$ of $G$ is also proper.
Sean English, Ping Zhang
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Alpha graphs with different pendent paths
Electronic Journal of Graph Theory and Applications, 2020 Graceful labelings are an effective tool to find cyclic decompositions of complete graphs and complete bipartite graphs. The strongest kind of graceful labeling, the α-labeling, is in the center of the research field of graph labelings, the existence of ...
Christian Barrientos
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A PROCEDURE FOR DERIVING ODD-GRACEFUL CHROMATIC NUMBERS OF GRAPHS
Ural Mathematical JournalLet \(G:=(V,E)\) be an undirected finite simple graph with vertex set \(V\) and edge set \(E\). A function \(c:V(G)\rightarrow \{1,2,\ldots,k\},\) for some positive integer \(k\), such that \(c(u)\neq c(v)\) for every edge \(uv\in E(G)\), is called a ...
I Nengah Suparta +3 more
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