Journals Information
Universal Journal of Applied Mathematics Vol. 12(3), pp. 78 - 83
DOI: 10.13189/ujam.2024.120302
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On Graph Representation of Bee's Dances
Araceli Gim茅nez Lorente *
Higher Education School of Art and Design, EASD (ISEACV), Castell贸 de la Plana, Spain
ABSTRACT
The application of graph theory in ethology is a relevant field, where the background of this study is focused only from the points of view of biology and chemistry. Our study is to find patterns in a specific behavior of bees, their dance. The purpose is to present the dance of bees as graphs, finding a mathematical character to animal ethology and a pattern that allows us to communicate with them. The methodology used is the observation of the dances of the hymenoptera through the viewing of videos, and bibliographic material. It is intended to analyze the communication of bees, translating their trajectory to the digraphs associated with the three different dances that we know, and through the associated matrix algebra, determine their homeomorphisms and main characteristics. The main result will be to extrapolate the schemes of the dances of the bees to directed graphs and their respective associated matrices to carry out a mathematical study. The dance of the bees is a very complex language that is analyzed with the digraphs in the sections that bear the name of the different dances, previously an introduction to these dances is made. Bees are capable of creating what we understand as a symbolic mathematical language to communicate. This is a point of connection with another intelligent species, and with the help of discrete mathematics, we can communicate; these results are partial since this study is preliminary, but necessary as a first phase. In the "discussion" section, some observations are made about this research and its possible implementation. Although this study of ethology from the mathematical point of view by approximation of graph theory is unprecedented, it is necessary for its possible future applications. For all these reasons, we see the need for this study.
KEYWORDS
Digraph Representation, Ethology, The Dance of Bees, Matrix Algebra
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Araceli Gim茅nez Lorente , "On Graph Representation of Bee's Dances," Universal Journal of Applied Mathematics, Vol. 12, No. 3, pp. 78 - 83, 2024. DOI: 10.13189/ujam.2024.120302.
(b). APA Format:
Araceli Gim茅nez Lorente (2024). On Graph Representation of Bee's Dances. Universal Journal of Applied Mathematics, 12(3), 78 - 83. DOI: 10.13189/ujam.2024.120302.