Cyclic Prime Graphicable Algebras
DOI:
https://doi.org/10.26713/cma.v13i5.2248Keywords:
Evolution algebra, Wheel graphicable algebra, Friendship graphicable algebra, Flower graphicable algebra, Jahangir graphicable algebraAbstract
This study constitutes the continuation of innovative research in Discrete Mathematics introduced in earlier research on algebras, in general regarding the utilization of graphs to contemplate the specific instance of graphicable algebras, which form a subset of evolution algebras. Group theory, stochastic processes, and dynamical systems are all naturally linked to evolution algebras, which makes them extremely interesting. In light of a new line of research initiated previously by some of the authors, a depiction on primeness of a certain type of graphicable and subgraphicable algebra is given.
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P. Cadavid, M. L. R. Montoya and P. M. Rodríguez, On the isomorphisms between evolution algebras of graphs and random walks, Linear and Multilinear Algebra 69(10) (2021), 1858 – 1877, DOI: 10.1080/03081087.2019.1645807.
L. M. Camacho, J. R. Gómez, B. A. Omirov and R. M. Turdibaev, Some properties of evolution algebras, Bulletin of the Korean Mathematical Society 50(5) (2013), 1481 – 1494, URL: https://www.math.uci.edu/~brusso/PropEvolAlgs2013Korea.pdf.
J. Clark and D. A. Holton, A First Look at Graph Theory, Allied Publishers Limited and World Scientific (1991), URL: https://inoerofik.files.wordpress.com/2014/11/firstlook_graphtheory.pdf.
J. Núñez, M. L. Rodríguez-Arévalo and M. T. Villar, Certain particular families of graphicable algebras, Applied Mathematics and Computation 246 (2014), 416 – 425, DOI: 10.1016/j.amc.2014.08.007.
J. Núñez, M. Silvero and M. T. Villar, Mathematical tools for the future: graph theory and graphicable algebras, Applied Mathematics and Computation 219(11) (2013), 6113 – 6125, DOI: 10.1016/j.amc.2012.12.004.
A. Rosa, On certain valuations of the vertices of a graph, In: International Symposium on Theory of Graphs, Rome (1966), 349 – 355, URL: http://www.cs.columbia.edu/~tim/teaching/cs4203/Rosa-GracefulLabelings.pdf.
J.-P. Tian and P. Vojtechovský, ˘ Evolution Algebras and their Applications, Lecture Notes in Mathematics, Vol. 1921, Springer-Verlag, Berlin, (2008), DOI: 10.1007/978-3-540-74284-5.
J.-P. Tian and P. Vojtechovský, Mathematical concepts of evolution algebra in non-mendelian genetics, Quasigroups and Related Systems 14(1) (2006), 111 – 122, URL: https://ibn.idsi.md/vizualizare_articol/8350.
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