{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T22:00:38Z","timestamp":1784066438072,"version":"3.55.0"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,9]],"date-time":"2023-10-09T00:00:00Z","timestamp":1696809600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Shannon entropy quantifying bi-colored Ramsey complete graphs is introduced and calculated for complete graphs containing up to six vertices. Complete graphs in which vertices are connected with two types of links, labeled as \u03b1-links and \u03b2-links, are considered. Shannon entropy is introduced according to the classical Shannon formula considering the fractions of monochromatic convex \u03b1-colored polygons with n\u00a0\u03b1-sides or edges, and the fraction of monochromatic \u03b2-colored convex polygons with m\u00a0\u03b2-sides in the given complete graph. The introduced Shannon entropy is insensitive to the exact shape of the polygons, but it is sensitive to the distribution of monochromatic polygons in a given complete graph. The introduced Shannon entropies S\u03b1 and S\u03b2 are interpreted as follows: S\u03b1 is interpreted as an average uncertainty to find the green \u03b1\u2212polygon in the given graph; S\u03b2 is, in turn, an average uncertainty to find the red \u03b2\u2212polygon in the same graph. The re-shaping of the Ramsey theorem in terms of the Shannon entropy is suggested. Generalization for multi-colored complete graphs is proposed. Various measures quantifying the Shannon entropy of the entire complete bi-colored graphs are suggested. Physical interpretations of the suggested Shannon entropies are discussed.<\/jats:p>","DOI":"10.3390\/e25101427","type":"journal-article","created":{"date-parts":[[2023,10,9]],"date-time":"2023-10-09T05:07:13Z","timestamp":1696828033000},"page":"1427","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Shannon Entropy of Ramsey Graphs with up to Six Vertices"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3025-6130","authenticated-orcid":false,"given":"Mark","family":"Frenkel","sequence":"first","affiliation":[{"name":"Chemical Engineering Department, Engineering Faculty, Ariel University, P.O.B. 3, Ariel 407000, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0582-4821","authenticated-orcid":false,"given":"Shraga","family":"Shoval","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Management, Faculty of Engineering, Ariel University, P.O.B. 3, Ariel 407000, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1356-2486","authenticated-orcid":false,"given":"Edward","family":"Bormashenko","sequence":"additional","affiliation":[{"name":"Chemical Engineering Department, Engineering Faculty, Ariel University, P.O.B. 3, Ariel 407000, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"84","DOI":"10.47443\/dml.2021.s110","article-title":"New directions in Ramsey theory","volume":"6","author":"Chartrand","year":"2021","journal-title":"Discrete Math. 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