Results 11 to 20 of about 828 (253)
Generating graceful unicyclic graphs from a given forest
AKCE International Journal of Graphs and Combinatorics, 2020 Acharya (1982) proved that every connected graph can be embedded in a graceful graph. The generalization of this result that, any set of graphs can be packed into a graceful graph was proved by Sethuraman and Elumalai (2005). Recently, Sethuraman et al. (
G. Sethuraman, V. Murugan
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Radio Graceful Labelling of Graphs
Theory and Applications of Graphs, 2020 Radio labelling problem of graphs have their roots in communication problem known as \emph{Channel Assignment Problem}. For a simple connected graph $G=(V(G), E(G))$, a radio labeling is a mapping $f \colon V(G)\rightarrow \{0,1,2,\ldots\}$ such that $|f(
Laxman Saha, Alamgir Basunia
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A structural approach to the graceful coloring of a subclass of trees [PDF]
Heliyon, 2023 Let M={1,2,..m} and G be a simple graph. A graceful m-coloring of G is a proper vertex coloring of G using the colors in M which leads to a proper edge coloring using M∖{m} colors such that the associated color of each edge is the absolute difference ...
Laavanya D, Devi Yamini S
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Discussiones Mathematicae Graph Theory, 2016 For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G) → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u) − f(v)| ≥ k + 1 − d(u, v). We consider k-radio labelings of G when k = diam(G).
Niedzialomski Amanda
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Electronic Notes in Discrete Mathematics, 2015 Abstract A total graceful labeling (TGL) of a ( p , q ) graph G is a bijection f from V ( G ) ∪ E ( G ) to the set { 1 , 2 , 3 , … , p + q } so that f ( u v ) = | f ( u ) − f ( v ) | for all u v ∈ E ( G ) . A TGL is called a super if f ( E ) = { 1 , 2 , 3 , … ,
S. P. Subbiah +2 more
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Additively graceful signed graphs
AKCE International Journal of Graphs and Combinatorics, 2023 Let [Formula: see text] be a signed graph of order p and size q. Let [Formula: see text] and [Formula: see text] Let [Formula: see text] be an injective function and let [Graphic: see text]gf(uv)={|f(u)−f(v)| if uv∈E+f(u)+f(v) if uv∈E−The function f is ...
Jessica Pereira +2 more
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Odd-Graceful Total Colorings for Constructing Graphic Lattice
Mathematics, 2021 The security of passwords generated by the graphic lattices is based on the difficulty of the graph isomorphism, graceful tree conjecture, and total coloring conjecture.
Jing Su, Hui Sun, Bing Yao
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Electronic Notes in Discrete Mathematics, 2009 Abstract Graph labeling of a graph was introduced by Rosa [A. Rosa, “Theory of graphs” (International Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967) 349-355] and the concept of an edge graceful labeling was introduced by Lo [S. Lo, “On edge graceful labeling of graphs”, Congress Numer., 50(1985) 231-241]. We introduced a
A Solairaju
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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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Edge Odd Graceful Labeling in Some Wheel-Related Graphs
MathematicsA graph’s edge labeling involves the allocation of symbols (colors or numbers) to the edges of a graph governed by specific criteria. Such labeling of a graph G with order n and size m is named edge odd graceful if there is a bijective map φ from the set
Mohammed Aljohani, Salama Nagy Daoud
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