{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T09:07:54Z","timestamp":1777367274632,"version":"3.51.4"},"reference-count":29,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,3]],"date-time":"2021-11-03T00:00:00Z","timestamp":1635897600000},"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>In this paper we introduce and study a new generalization of Fibonacci polynomials which generalize Fibonacci, Jacobsthal and Narayana numbers, simultaneously. We give a graph interpretation of these polynomials and we obtain a binomial formula for them. Moreover by modification of Pascal\u2019s triangle, which has a symmetric structure, we obtain matrices generated by coefficients of generalized Fibonacci polynomials. As a consequence, the direct formula for generalized Fibonacci polynomials was given. In addition, we determine matrix generators for generalized Fibonacci polynomials, using the symmetric matrix of initial conditions.<\/jats:p>","DOI":"10.3390\/sym13112075","type":"journal-article","created":{"date-parts":[[2021,11,3]],"date-time":"2021-11-03T21:57:49Z","timestamp":1635976669000},"page":"2075","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Distance Fibonacci Polynomials by Graph Methods"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8887-4321","authenticated-orcid":false,"given":"Dominik","family":"Strza\u0142ka","sequence":"first","affiliation":[{"name":"Faculty of Electrical and Computer Engineering, Rzesz\u00f3w University of Technology, Aleja Powsta\u0144c\u00f3w Warszawy 12, 35-959 Rzesz\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8968-0959","authenticated-orcid":false,"given":"S\u0142awomir","family":"Wolski","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Applied Physics, Rzesz\u00f3w University of Technology, Aleja Powsta\u0144c\u00f3w Warszawy 12, 35-959 Rzesz\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1789-6280","authenticated-orcid":false,"given":"Andrzej","family":"W\u0142och","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Applied Physics, Rzesz\u00f3w University of Technology, Aleja Powsta\u0144c\u00f3w Warszawy 12, 35-959 Rzesz\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,3]]},"reference":[{"key":"ref_1","first-page":"139","article-title":"The Total Number of Generalized Stable Sets and Kernels in Graphs","volume":"55","year":"2000","journal-title":"Ars Comb."},{"key":"ref_2","unstructured":"Szynal-Liana, A., and W\u0142och, I. 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