{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T14:56:38Z","timestamp":1746802598180,"version":"3.40.5"},"reference-count":32,"publisher":"Wiley","license":[{"start":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T00:00:00Z","timestamp":1672790400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100019812","name":"Tishreen University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100019812","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2023,1,4]]},"abstract":"<jats:p>Topological polynomial and indices based on the distance between the vertices of a connected graph are widely used in the chemistry to establish relation between the structure and the properties of molecules. In a similar way, chromatic versions of certain topological indices and the related polynomial have also been discussed in the recent literature. In this paper, we present the chromatic Schultz and Gutman polynomials and the expanded form of the Hosoya polynomial and chromatic Schultz and Gutman polynomials, and then we derive these polynomials for special cases of Jahangir graphs.<\/jats:p>","DOI":"10.1155\/2023\/4891083","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T20:50:13Z","timestamp":1672865413000},"page":"1-13","source":"Crossref","is-referenced-by-count":3,"title":["Chromatic Schultz and Gutman Polynomials of Jahangir Graphs <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                     <a:msub>\n                        <a:mrow>\n                           <a:mi>J<\/a:mi>\n                        <\/a:mrow>\n                        <a:mrow>\n                           <a:mn>2<\/a:mn>\n                           <a:mo>,<\/a:mo>\n                           <a:mi>m<\/a:mi>\n                        <\/a:mrow>\n                     <\/a:msub>\n                  <\/a:math> and <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                     <c:msub>\n                        <c:mrow>\n                           <c:mi>J<\/c:mi>\n                        <\/c:mrow>\n                        <c:mrow>\n                           <c:mn>3<\/c:mn>\n                           <c:mo>,<\/c:mo>\n                           <c:mi>m<\/c:mi>\n                        <\/c:mrow>\n                     <\/c:msub>\n                  <\/c:math>"],"prefix":"10.1155","volume":"2023","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8515-6498","authenticated-orcid":true,"given":"Ramy","family":"Shaheen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science Tishreen University, Lattakia, Syria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9747-9668","authenticated-orcid":true,"given":"Suhail","family":"Mahfud","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science Tishreen University, Lattakia, Syria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2579-0806","authenticated-orcid":true,"given":"Qays","family":"Alhawat","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science Tishreen University, Lattakia, Syria"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1021\/cr0004456"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1021\/cr9903656"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1021\/ja01193a005"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02704315"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1080\/07391102.2006.10507094"},{"key":"6","first-page":"13","article-title":"Some properties of the Wiener polynomials","volume":"125","author":"I. Gutman","year":"1993","journal-title":"Graph theory notes of New York"},{"key":"7","first-page":"93","article-title":"M-polynomial, and degree-based topological indices","volume":"6","author":"E. Deutsch","year":"2015","journal-title":"Iranian Journal of Mathematical Chemistry"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.3390\/sym8090097"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.3390\/sym8110134"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.3390\/sym9010017"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.3390\/sym8120149"},{"key":"12","first-page":"807","article-title":"Hosoya polynomial of pentachains","volume":"65","author":"A. A. Ali","year":"2011","journal-title":"MATCH Communications in Mathematical and Computer Chemistry"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1021\/ci9501857"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1021\/ci00063a012"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1021\/ci9603689"},{"issue":"1","key":"16","first-page":"233","article-title":"Extended cut method for edge Wiener, Schultz and Gutman indices with applications","volume":"76","author":"M. Arockiaraj","year":"2016","journal-title":"MATCH Communications in Mathematical and Computer Chemistry"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1007\/s10910-016-0646-3"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.molstruc.2020.128368"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1080\/00268976.2020.1798529"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.4236\/am.2015.614204"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2011.04.002"},{"key":"22","first-page":"12","article-title":"Modified chromatic Schultz polynomial of some cycle related graph","volume":"27","author":"R. Raja","year":"2019","journal-title":"Acta Universitatis Matthiae Belii, series Mathematics"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.4067\/s0716-09172015000200005"},{"key":"24","first-page":"1","article-title":"Hosoya polynomial and Wiener index of Jahangir graphs J2,m","volume":"7","author":"M. R. Farahani","year":"2015","journal-title":"Pacific Journal of Applied Mathematics"},{"key":"25","first-page":"91","article-title":"The Wiener index and Hosoya polynomial of a class of Jahangir graphs J3,m","volume":"3","author":"M. R. Farahani","year":"2015","journal-title":"Fundamentant Journal of Mathematics and Mathematical Sciences"},{"key":"26","first-page":"232","article-title":"Hosoya polynomial of Jahangir graphs J4,m","volume":"3","author":"M. R. Farahani","year":"2015","journal-title":"Global Journal of Mathematics"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.11648\/j.acm.20160503.17"},{"key":"28","first-page":"30","article-title":"Computation of Hosoya polynomial, Wiener and hyper Wiener J6,m","volume":"13","author":"M. Rezaei","year":"2017","journal-title":"Journal of Prime Research in Mathematics"},{"key":"29","first-page":"1","article-title":"Hosoya polynomial and topological indices of the Jahangir graphs J7,m","volume":"7","author":"A. R. Nizami","year":"2018","journal-title":"Journal Applied & Computational Mathematics"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.4236\/am.2016.714140"},{"key":"31","first-page":"823","article-title":"The Schultz polynomial, modified Schultz polynomial of the Jahangir graphs Jn,m for integer number n=3","volume":"3","author":"M. R. Farahani","year":"2015","journal-title":"Asian Journal of Applied Sciences"},{"key":"32","first-page":"823","article-title":"The Schultz polynomial, modified Schultz polynomial and their indices for the Jahangir graphs J4,m for integer number n=4","volume":"3","author":"S. Wang","year":"2015","journal-title":"Asian Journal of Applied Sciences"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2023\/4891083.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2023\/4891083.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2023\/4891083.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T20:50:28Z","timestamp":1672865428000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/jam\/2023\/4891083\/"}},"subtitle":[],"editor":[{"given":"Sheng","family":"Zhang","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2023,1,4]]},"references-count":32,"alternative-id":["4891083","4891083"],"URL":"https:\/\/doi.org\/10.1155\/2023\/4891083","relation":{},"ISSN":["1687-0042","1110-757X"],"issn-type":[{"type":"electronic","value":"1687-0042"},{"type":"print","value":"1110-757X"}],"subject":[],"published":{"date-parts":[[2023,1,4]]}}}