{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T08:25:13Z","timestamp":1774945513985,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,8,19]],"date-time":"2020-08-19T00:00:00Z","timestamp":1597795200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Apart from its applications in Chemistry, Biology, Physics, Social Sciences, Anthropology, etc., there are close relations between graph theory and other areas of Mathematics. Fibonacci numbers are of utmost interest due to their relation with the golden ratio and also due to many applications in different areas from Biology, Architecture, Anatomy to Finance. In this paper, we define Fibonacci graphs as graphs having degree sequence consisting of n consecutive Fibonacci numbers and use the invariant \u03a9 to obtain some more information on these graphs. We give the necessary and sufficient conditions for the realizability of a set D of n successive Fibonacci numbers for every n and also list all possible realizations called Fibonacci graphs for 1\u2264n\u22644.<\/jats:p>","DOI":"10.3390\/sym12091383","type":"journal-article","created":{"date-parts":[[2020,8,19]],"date-time":"2020-08-19T21:37:40Z","timestamp":1597873060000},"page":"1383","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Fibonacci Graphs"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8873-1999","authenticated-orcid":false,"given":"Aysun","family":"Yurttas Gunes","sequence":"first","affiliation":[{"name":"Mathematics Department, Bursa Uludag University, Gorukle, 16059 Bursa, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4689-3660","authenticated-orcid":false,"given":"Sadik","family":"Delen","sequence":"additional","affiliation":[{"name":"Mathematics Department, Bursa Uludag University, Gorukle, 16059 Bursa, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6439-8439","authenticated-orcid":false,"given":"Musa","family":"Demirci","sequence":"additional","affiliation":[{"name":"Mathematics Department, Bursa Uludag University, Gorukle, 16059 Bursa, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7539-5065","authenticated-orcid":false,"given":"Ahmet Sinan","family":"Cevik","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Selcuk University, 42075 Konya, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0700-5774","authenticated-orcid":false,"given":"Ismail Naci","family":"Cangul","sequence":"additional","affiliation":[{"name":"Mathematics Department, Bursa Uludag University, Gorukle, 16059 Bursa, Turkey"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,19]]},"reference":[{"key":"ref_1","first-page":"131","article-title":"On some applications of graph theory to number theoretic problems","volume":"1","year":"1969","journal-title":"Publ. 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Ser."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Koshy, T. (2001). Fibonacci and Lucas Numbers with Applications, John Wiley and Sons.","DOI":"10.1002\/9781118033067"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"30","DOI":"10.12691\/tjant-6-1-4","article-title":"A New Graph Invariant","volume":"6","author":"Delen","year":"2018","journal-title":"Turk. J. Anal. Number Theory"},{"key":"ref_8","first-page":"14","article-title":"The Effect of Edge and Vertex Deletion on Omega Invariant","volume":"2020","author":"Delen","year":"2020","journal-title":"Appl. Anal. Discr. Math."},{"key":"ref_9","first-page":"91","article-title":"Omega Invariant of Graphs and Cyclicness","volume":"21","author":"Delen","year":"2019","journal-title":"Appl. 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Introduction to Graph Theory, Pearson."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/9\/1383\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:02:49Z","timestamp":1760176969000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/9\/1383"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,19]]},"references-count":15,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["sym12091383"],"URL":"https:\/\/doi.org\/10.3390\/sym12091383","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,19]]}}}