{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:30:06Z","timestamp":1747189806912,"version":"3.40.5"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,8]]},"abstract":"<jats:p> Three vertices [Formula: see text] in a graph [Formula: see text] are said to be [Formula: see text]-sequent if [Formula: see text] and [Formula: see text] are adjacent edges in [Formula: see text]. A 3-sequent coloring (3s coloring) is a function [Formula: see text] such that if [Formula: see text] and [Formula: see text] are 3-sequent vertices, then either [Formula: see text] or [Formula: see text] (or both). The [Formula: see text]-sequent achromatic number of a graph [Formula: see text], denoted [Formula: see text], equals the maximum number of colors that can be used in a coloring of the vertices\u2019 of [Formula: see text] such that if [Formula: see text] and [Formula: see text] are any two sequent edges in [Formula: see text], then either [Formula: see text] or [Formula: see text] is colored the same as [Formula: see text]. The [Formula: see text]-sequent achromatic sum of a graph [Formula: see text], denoted [Formula: see text], is the greatest sum of colors among all proper 3s-coloring that requires [Formula: see text] colors. This research initiates the study of [Formula: see text]-sequent achromatic sum and finds the exact values of this parameter for some known graphs. Furthermore, we calculate the [Formula: see text] of corona product, Cartesian product of the graphs and some important results have been proved and a comparative study is carried out. <\/jats:p>","DOI":"10.1142\/s1793830921500397","type":"journal-article","created":{"date-parts":[[2020,12,3]],"date-time":"2020-12-03T09:59:09Z","timestamp":1606989549000},"page":"2150039","source":"Crossref","is-referenced-by-count":0,"title":["3-Sequent achromatic sum of graphs"],"prefix":"10.1142","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1321-7076","authenticated-orcid":false,"given":"Charles","family":"Dominic","sequence":"first","affiliation":[{"name":"Department of Mathematics, CHRIST (Deemed to be University), Bangalore 560029, Karnataka, India"}]},{"given":"Jobish Vallikavungal","family":"Devassia","sequence":"additional","affiliation":[{"name":"Tecnologico de Monterrey, School of Engineering and Sciences, Mexico"}]}],"member":"219","published-online":{"date-parts":[[2020,12,3]]},"reference":[{"key":"S1793830921500397BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.04.006"},{"key":"S1793830921500397BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2010.11.004"},{"key":"S1793830921500397BIB003","doi-asserted-by":"publisher","DOI":"10.7151\/dmgt.1502"},{"volume-title":"Zero-Symmetric Graphs: Trivalent Graphical Regular Representations of Groups","year":"2014","author":"Coxeter H. S. M.","key":"S1793830921500397BIB004"},{"key":"S1793830921500397BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/BF01844162"},{"key":"S1793830921500397BIB006","doi-asserted-by":"publisher","DOI":"10.7151\/dmgt.1814"},{"key":"S1793830921500397BIB007","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"key":"S1793830921500397BIB008","first-page":"559","volume":"29","author":"Koh R. D. G.","year":"1980","journal-title":"Congr. Numer."},{"key":"S1793830921500397BIB009","doi-asserted-by":"publisher","DOI":"10.1145\/75427.75430"},{"key":"S1793830921500397BIB011","first-page":"161","volume-title":"Proc. ICDM","author":"Sampathkumar E.","year":"2008"},{"key":"S1793830921500397BIB012","doi-asserted-by":"publisher","DOI":"10.1109\/71.629486"},{"key":"S1793830921500397BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2009.05.018"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830921500397","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,12]],"date-time":"2021-07-12T09:06:12Z","timestamp":1626080772000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830921500397"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,3]]},"references-count":12,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["10.1142\/S1793830921500397"],"URL":"https:\/\/doi.org\/10.1142\/s1793830921500397","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2020,12,3]]}}}