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Czechoslovak Mathematical Journal, 2004
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Acharya, Mukti, Singh, Tarkeshwar
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Acharya, Mukti, Singh, Tarkeshwar
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ODD GRACEFUL LABELINGS OF GRAPHS
Discrete Mathematics, Algorithms and Applications, 2009A graph G = (V(G), E(G)) with q edges is said to be odd graceful if there exists an injection f from V(G) to {0, 1, 2, …, 2q - 1} such that the edge labeling set is {1, 3, 5, …, 2q - 1} with each edge xy assigned the label |f(x) - f(y)|. In this paper, we prove that Pn × Pm (m = 2, 3, 4), generalized crown graphs Cn ⊙ K1,t and gear graphs are odd ...
Zhen-Bin Gao +2 more
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On Modular Edge-Graceful Graphs
Graphs and Combinatorics, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Futaba Fujie-Okamoto +3 more
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2016
Let $$G=V,E$$ be a p,i¾źq-graph without isolated vertices. The gracefulness gracG of G is the smallest positive integer k for which there exists an injective function $$f:V\rightarrow \{0,1,2,\dots , k\}$$ such that the edge induced function $$g_f:E\rightarrow \{1,2,\dots , k\}$$ defined by $$g_fuv=|fu-fv|$$, $$\forall uv \in E$$ is also injective. Let
Jessica Pereira +2 more
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Let $$G=V,E$$ be a p,i¾źq-graph without isolated vertices. The gracefulness gracG of G is the smallest positive integer k for which there exists an injective function $$f:V\rightarrow \{0,1,2,\dots , k\}$$ such that the edge induced function $$g_f:E\rightarrow \{1,2,\dots , k\}$$ defined by $$g_fuv=|fu-fv|$$, $$\forall uv \in E$$ is also injective. Let
Jessica Pereira +2 more
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Constraint models for graceful graphs
Constraints, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Barbara M. Smith, Jean-François Puget
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Aequationes mathematicae, 2022
Graceful labeling and antimagic labeling are two significant topics in the domain of graph labelings, with outstanding conjectures which still remain unsolved. In this paper, the authors combine these two concepts to define a new labeling, called graceful antimagic labelings. Graceful antimagicness of some families of trees, cycles, and nearly complete
Mohammed Ali Ahmed +4 more
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Graceful labeling and antimagic labeling are two significant topics in the domain of graph labelings, with outstanding conjectures which still remain unsolved. In this paper, the authors combine these two concepts to define a new labeling, called graceful antimagic labelings. Graceful antimagicness of some families of trees, cycles, and nearly complete
Mohammed Ali Ahmed +4 more
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Edge consecutive gracefulness of a graph
Discrete Applied Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jessica Pereira +2 more
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JP Journal of Algebra, Number Theory and Applications, 2019
A simple, connected graph \(G(V,E)\) is graceful [\textit{J. A. Gallian}, Electron. J. Comb. DS06, Research paper DS6, 43 p. (1998; Zbl 0953.05067)] if there exists an injective mapping \(f:V\to\{0,1,\dots,|V|\}\), under which all differences in \(\{|f(u)-f(v)|:uv\in E\}\) are distinct. In the \(n\times m\) geometrical king's graph (representing king's
Susanti, Yeni +4 more
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A simple, connected graph \(G(V,E)\) is graceful [\textit{J. A. Gallian}, Electron. J. Comb. DS06, Research paper DS6, 43 p. (1998; Zbl 0953.05067)] if there exists an injective mapping \(f:V\to\{0,1,\dots,|V|\}\), under which all differences in \(\{|f(u)-f(v)|:uv\in E\}\) are distinct. In the \(n\times m\) geometrical king's graph (representing king's
Susanti, Yeni +4 more
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Symmetry Breaking in Graceful Graphs
2003Symmetry occurs frequently in Constraint Satisfaction Problems (CSPs). For instance, in 3-colouring the nodes of a graph, a CSP model that assigns a specific colour to each node has sets of equivalent solutions in which the three colours are permuted.
Karen E. Petrie, Barbara M. Smith
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Journal of Discrete Mathematical Sciences and Cryptography, 2010
Abstract A (p, q)-graph G = (V, E) is called vertex-graceful if it admits a vertex-graceful numbering, which is defined as an injection f : E → {0, 1, 2,…, q*}, q* = max{p, q} such that the function fV : V → ℕ defined by the rule fV (v) = max{f (e) : e ∈ Ev and v ∈ e}.-min {f(e) : e ∈ Ev and v ∈ e} satisfies the property that fV (V) ≔ {fV (u) : u ∈ V} =
B. D. Acharya, K. A. Germina
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Abstract A (p, q)-graph G = (V, E) is called vertex-graceful if it admits a vertex-graceful numbering, which is defined as an injection f : E → {0, 1, 2,…, q*}, q* = max{p, q} such that the function fV : V → ℕ defined by the rule fV (v) = max{f (e) : e ∈ Ev and v ∈ e}.-min {f(e) : e ∈ Ev and v ∈ e} satisfies the property that fV (V) ≔ {fV (u) : u ∈ V} =
B. D. Acharya, K. A. Germina
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