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- W2183625504 abstract "Coprime labelings and Coprime graphs have been of interest since 1980s and got popularized by the Entringer-Tout Tree Conjecture. Around the same time Newman‘s coprime mapping conjecture was settled by Pomerance and Selfridge. This result was further extended to integers in arithmetic progression. Since then coprime graphs were studied for various combinatorial properties. Here, coprimality of graphs for classes of graphs under the themes: Bipartite with special attention to Acyclicity, Eulerian and Regularity. Extremal graphs under non-coprimality and Eulerian properties are studied. Embeddings of coprime graphs in the general graphs, the maximum coprime graph and the Eulerian coprime graphs are studied as subgraphs and induced subgraphs. The purpose of this review is to assimilate the available works on coprime graphs. The results in the context of these themes are reviewed including embeddings and extremal problems. Terminology The terms coprime labelings or coprime graphs are used throughout the paper as was also used by P. Erdos, G.N. Sarkozy (1997) which otherwise are known as prime lebelings and prime graphs in the literature. The term coprime justifies the nomenclature in the definition based on the coprimality. This also avoids the confusion with other types of prime graphs defined in the literature in other contexts based on the primality." @default.
- W2183625504 created "2016-06-24" @default.
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- W2183625504 date "2011-01-01" @default.
- W2183625504 modified "2023-10-17" @default.
- W2183625504 title "A Creative Review on Coprime (Prime) Graphs" @default.
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