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Prime labelings on planar grid graphs [PDF]
Theory and Applications of Graphs, 2022 It is known that for any prime p and any integer n such that 1≤n≤p there exists a prime labeling on the pxn planar grid graph PpxPn.
Stephen James Curran
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Prime labelings on a 3xn grid graph
Theory and Applications of GraphsIt is conjectured that the mxn grid graph has a prime labeling for all positive integers m and n. It is known that for any prime p and any integer n such that 1≤n≤p2, there exists a prime labeling on the pxn grid graph Pm x Pn. Also, it is known that the
Stephen J. Curran, Matt A. Ollis
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Prime and Odd Prime Labelings on Cycle-Related Graphs
Science and Technology IndonesiaGraph labeling is the process of determining integer values for vertices, edges, or both, based on certain criteria. Let G be a simple graph with the finite vertex set V(G). Prime labeling of G is a bijection ⍺:V(G)→{1,2,…,|V(G)|} for which each pair of
Hafif Komarullah +3 more
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Application of the Combinatorial Nullstellensatz to Integer-magic Graph Labelings [PDF]
Theory and Applications of Graphs, 2022 Let $A$ be a nontrivial abelian group and $A^* = A \setminus \{0\}$. A graph is $A$-magic if there exists an edge labeling $f$ using elements of $A^*$ which induces a constant vertex labeling of the graph.
Richard Low, Dan Roberts
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Discrete Mathematics, 1994 The paper is devoted to the study of prime graphs, that is finite graphs that admit a prime labelling. A prime labelling of a graph \(G=(V,E)\) is a bijection \(f: V\to \{1,2,\dots,| V|\}\) such that if \(e= \{u,v\}\in E\) then \(\text{GCD}(f(u),f(v))= 1\). Some results concerning bipartite graphs are obtained; all trees of order up to 15 are proved to
Hung-Lin Fu, Kuo-Ching Huang
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Prime Labelings of Snake Graphs [PDF]
The PUMP Journal of Undergraduate Research, 2019 A prime labeling of a graph G with n vertices is a labeling of the vertices with distinct integers from the set {1, 2 ,..., n} such that the labels of any two adjacent vertices are relatively prime. In this paper, we introduce a snake graph, the fused union of identical cycles, and define a consecutive snake prime labeling for this new family of graphs.
Abigail Bigham +4 more
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Prime labelings of infinite graphs
Involve, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Oscar Levin
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Frequency Assignment Model of Zero Divisor Graph
Journal of Applied Mathematics, 2021 Given a frequency assignment network model is a zero divisor graph Γ=V,E of commutative ring Rη, in this model, each node is considered to be a channel and their labelings are said to be the frequencies, which are assigned by the L2,1 and L3,2,1 labeling
R. Radha, N. Mohamed Rilwan
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Journal of Mathematics, 2023 In this article, we adapt the edge-graceful graph labeling definition into block designs and define a block design V,B with V=v and B=b as block-graceful if there exists a bijection f:B⟶1,2,…,b such that the induced mapping f+:V⟶Zv given by f+x=∑x∈AA ...
Dilara Erdemir, Emre Kolotoğlu
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