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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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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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ON PRONIC GRACEFULNESS OF GRAPHS
2023Let G be a graph of order p and size q. A graceful labeling of G is an injection f : V → {0,1,...,q}such that while each edge uv is assigned the label(absolute difference of the corresponding vertex labels), the induced edge labels are all distinct.
S. Akila Devi, V. Jayapriya
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Journal of Graph Theory, 1980
AbstractWe give graceful numberings to the following graphs: (a) the union of n K4 having one edge in common, in other words the join of K2 and the union of n disjoint K2 and (b) the union of n C4 having one edge in common, in other words the product of K2 and K1,n, with n + 1 not a multiple of 4.
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AbstractWe give graceful numberings to the following graphs: (a) the union of n K4 having one edge in common, in other words the join of K2 and the union of n disjoint K2 and (b) the union of n C4 having one edge in common, in other words the product of K2 and K1,n, with n + 1 not a multiple of 4.
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All Uniform Bow Graphs are Graceful
Mathematics in Computer Science, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J. Jeba Jesintha, K. Ezhilarasi Hilda
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