{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T01:12:17Z","timestamp":1767575537662,"version":"3.41.2"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100001843","name":"Science and Engineering Research Board","doi-asserted-by":"publisher","award":["EMR\/2017\/001869"],"award-info":[{"award-number":["EMR\/2017\/001869"]}],"id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,10]]},"abstract":"<jats:p> The total chromatic number [Formula: see text] is the least number of colors needed to color the vertices and edges of a graph [Formula: see text] such that no incident or adjacent elements (vertices or edges) receive the same color. Behzad and Vizing proposed a well-known total coloring conjecture (TCC): [Formula: see text], where [Formula: see text] is the maximum degree of [Formula: see text]. For the powers of cycles, Campos and de Mello proposed the following conjecture: Let [Formula: see text] denote the graphs of powers of cycles of order [Formula: see text] and length [Formula: see text] with [Formula: see text]. Then, [Formula: see text] In this paper, we prove the Campos and de Mello\u2019s conjecture for some classes of powers of cycles. Also, we prove the TCC for complement of powers of cycles. <\/jats:p>","DOI":"10.1142\/s1793830921500506","type":"journal-article","created":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T04:16:37Z","timestamp":1604290597000},"source":"Crossref","is-referenced-by-count":8,"title":["Total colorings of circulant graphs"],"prefix":"10.1142","volume":"13","author":[{"given":"J.","family":"Geetha","sequence":"first","affiliation":[{"name":"Department of Mathematics, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, Coimbatore, India"}]},{"given":"K.","family":"Somasundaram","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, Coimbatore, India"}]},{"given":"Hung-Lin","family":"Fu","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30010, Taiwan"}]}],"member":"219","published-online":{"date-parts":[[2020,12,7]]},"reference":[{"key":"S1793830921500506BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-21919-1"},{"key":"S1793830921500506BIB003","first-page":"1","volume-title":"Proc, Conf. Combinatorial Mathematics and Its Applications, Oxford 1969","author":"Behzad M.","year":"1971"},{"key":"S1793830921500506BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2006.08.010"},{"issue":"2","key":"S1793830921500506BIB006","first-page":"177","volume":"4","author":"Campos C. N.","year":"2003","journal-title":"Tendencias em Matematica Aplicada e Computacional"},{"key":"S1793830921500506BIB007","first-page":"195","volume":"66","author":"Chetwynd A. G.","year":"1988","journal-title":"Congr. Numer."},{"key":"S1793830921500506BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.11.070"},{"key":"S1793830921500506BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(92)00058-Y"},{"key":"S1793830921500506BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(89)90187-8"},{"key":"S1793830921500506BIB011","first-page":"25","volume":"3","author":"Vizing V. G.","year":"1964","journal-title":"Diskret. Anal."},{"key":"S1793830921500506BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0092895"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830921500506","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,14]],"date-time":"2021-10-14T03:59:49Z","timestamp":1634183989000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830921500506"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,7]]},"references-count":10,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["10.1142\/S1793830921500506"],"URL":"https:\/\/doi.org\/10.1142\/s1793830921500506","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2020,12,7]]},"article-number":"2150050"}}