In this paper we provide some sufficient conditions for the Cartesian product of graphs to beH-antimagic.We use partitions subsets of integers for describing desiredH-antimagic labelings.
📌 3 Key Takeaways
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Objective & Hypothesis:A graphG= (V(G);E(G)) admits anH-covering if every edge inEbelongs to a subgraph ofGisomorphic toH.
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Key Findings & Data:A graphGadmitting anH-covering is called (a;d)-H-antimagicif there is a bijectionf:V(G)[E(G)!f1;2;:::;jV(G)j+jE(G)jgsuch that, for all subgraphsH′ofGisomorphic toH, theH-weights,wtf(H′) =∑v2V(H′)f(v)+∑e2E(H′)f(e);constitute an arithmetic progression with the initial termaand the commondifferenced.
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Conclusion & Impact:In this paper we provide some sufficient conditions for the Cartesian product of graphs to beH-antimagic.We use partitions subsets of integers for describing desiredH-antimagic labelings.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
A graphG= (V(G);E(G)) admits anH-covering if every edge inEbelongs to a subgraph ofGisomorphic toH. A graphGadmitting anH-covering is called (a;d)-H-antimagicif there is a bijectionf:V(G)[E(G)!f1;2;:::;jV(G)j+jE(G)jgsuch that, for all subgraphsH′ofGisomorphic toH, theH-weights,wtf(H′) =∑v2V(H′)f(v)+∑e2E(H′)f(e);constitute an arithmetic progression with the initial termaand the commondifferenced. In this paper we provide some sufficient conditions for the Cartesian product of graphs to beH-antimagic.We use partitions subsets of integers for describing desiredH-antimagic labelings.
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Cite This Article
BACA, M., SEMANICOVA-FENOVCIKOV, A., UMAR, M. A., WELYYANTI, D. (2022). OnH-antimagicness of Cartesian product of graphs. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 1, 339–348. https://ajindex.com/articles/607763
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