Results 231 to 240 of about 1,000,377 (259)
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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 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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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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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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Graceful graphs with pendant edges [PDF]
Australas. J Comb., 2005 The author gives graceful labelings for the graphs \(G+ nK\), and \(G\odot nK\), where \(G\) is a graceful graph whose order is greater than its size. He also provides a graceful labeling for the unicyclic graph formed when an arbitrary number of pendant edges are attached to a cycle.
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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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Gracefulness of the join of graceful graph and path
AIP Conference Proceedings, 2023Luthfan Fawwaz +3 more
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The graph SSG(2) is odd graceful and odd harmonious
International Journal of Computer Aided Engineering and Technology, 2021J. Jesintha, K. Hilda
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New families of graceful graphs.
Ars Comb., 2003The gracefulness of graphs obtained by the join and union operations is studied. Particularly, the classes \(G\, \cup \, H\) (\(G\) is \(\alpha \)-labeled, \(H\) is pseudograceful), \(G+\overline K_n\) (\(G\) is a Skolem-graceful graph), \(\overline K_n+mK_2\) and \(C_m\cup S_n\) (\(S_n\) is a star on \(n+1\) vertices) are discussed.
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Two classes of graceful graphs
Ars Comb., 2000A graph is graceful if it allows a labelling \(\varphi \) of its vertices by distinct nonnegative integers such that, for edges \(uv\), \(|\varphi (u)-\varphi (v)|\) attains all values from \(\{1,2,\dots ,q\}\), where \(q\) is the number of edges. This paper identifies two new classes of graceful graphs.
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