{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:22:02Z","timestamp":1753881722205,"version":"3.41.2"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:p> A b-coloring of a graph [Formula: see text] is a proper coloring of the vertices of [Formula: see text] such that there exist a vertex in each color class joined to at least one vertex in each other color classes. The b-chromatic number of a graph [Formula: see text], denoted by [Formula: see text], is the largest integer [Formula: see text] such that [Formula: see text] has a b-coloring with [Formula: see text] colors. The b-chromatic sum of a graph [Formula: see text], denoted by [Formula: see text], is introduced and it is defined as the minimum of sum of colors [Formula: see text] of [Formula: see text] for any [Formula: see text] in a b-coloring of [Formula: see text] using [Formula: see text] colors. A graph [Formula: see text] is b-continuous, if it admits a b-coloring with [Formula: see text] colors, for every [Formula: see text]. In this paper, the [Formula: see text]-continuity property of corona of two cycles, corona of two star graphs and corona of two wheel graphs with unequal number of vertices is discussed. The b-continuity property of corona of any two graphs with same number of vertices is also discussed. Also, the b-continuity property of Mycielskian of complete graph, complete bipartite graph and paths are discussed. The b-chromatic sum of power graph of a path is also obtained. <\/jats:p>","DOI":"10.1142\/s0219265921500122","type":"journal-article","created":{"date-parts":[[2021,7,27]],"date-time":"2021-07-27T15:36:43Z","timestamp":1627400203000},"source":"Crossref","is-referenced-by-count":0,"title":["b-Chromatic Sum and b-Continuity Property of Some Graphs"],"prefix":"10.1142","volume":"21","author":[{"given":"P. C.","family":"Lisna","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Advanced Sciences (SAS), VIT-AP University, Amaravati, Andhra Pradesh 522237, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. S.","family":"Sunitha","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Institute of Technology, Calicut \u2013 673 601, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,10,12]]},"reference":[{"key":"S0219265921500122BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-008-0829-1"},{"key":"S0219265921500122BIB002","doi-asserted-by":"publisher","DOI":"10.1109\/ICDAR.2009.72"},{"key":"S0219265921500122BIB003","first-page":"0045","volume":"6","author":"Effantin B.","year":"2003","journal-title":"Discr. Math. Theoret. Comput. Sci."},{"volume-title":"About b-Coloring of Regular Graphs","year":"2006","author":"Sahili A. El","key":"S0219265921500122BIB004"},{"key":"S0219265921500122BIB005","first-page":"228","volume-title":"Proceedings of GbR2007","author":"Elghazel H.","year":"2007"},{"volume-title":"Chromatic Graph Theory","year":"2009","author":"Chartrand G.","key":"S0219265921500122BIB006"},{"key":"S0219265921500122BIB007","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"volume-title":"Distance in Graphs","year":"1990","author":"Buckley F.","key":"S0219265921500122BIB008"},{"key":"S0219265921500122BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(98)00146-2"},{"key":"S0219265921500122BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s00010-013-0207-9"},{"key":"S0219265921500122BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2009.01.017"},{"issue":"3","key":"S0219265921500122BIB012","first-page":"1550040-1","volume":"7","author":"Lisna P. C.","year":"2015","journal-title":"Discr. Math. Algorithms Appl."},{"issue":"1","key":"S0219265921500122BIB013","first-page":"1550004-1","volume":"15","author":"Lisna P. C.","year":"2015","journal-title":"J. Interconnection Networks"},{"key":"S0219265921500122BIB014","doi-asserted-by":"publisher","DOI":"10.1504\/IJCONVC.2016.080395"},{"key":"S0219265921500122BIB015","doi-asserted-by":"publisher","DOI":"10.4064\/cm-3-2-161-162"},{"key":"S0219265921500122BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2011.04.028"},{"key":"S0219265921500122BIB017","doi-asserted-by":"publisher","DOI":"10.5772\/6099"},{"key":"S0219265921500122BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/s40010-013-0074-8"},{"key":"S0219265921500122BIB019","first-page":"295","volume-title":"Ricerche di Mathematica","volume":"63","author":"Venkatachalam M.","year":"2014"},{"issue":"5","key":"S0219265921500122BIB020","first-page":"443","volume":"17","author":"Vivin J. Vernold","year":"2014","journal-title":"Journal of Discr. Math. Sci. Cryptography-Taylor and Francis"},{"journal-title":"J. Egyptian Mathematical Society","year":"2014","author":"Vivin J. Vernold","key":"S0219265921500122BIB021"},{"key":"S0219265921500122BIB022","first-page":"299","volume":"88","author":"Vivin J. Vernold","year":"2012","journal-title":"Utilitas Mathematica"},{"issue":"4","key":"S0219265921500122BIB023","first-page":"1439","volume":"3","author":"Vijayalakshmi D.","year":"2012","journal-title":"Int. J. Mathematical Archive"},{"issue":"4","key":"S0219265921500122BIB024","first-page":"715","volume":"1","author":"Vijayalakshmi D.","year":"2012","journal-title":"Int. J. Appl. Math. Res."},{"key":"S0219265921500122BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2013.05.024"}],"container-title":["Journal of Interconnection Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219265921500122","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,18]],"date-time":"2021-10-18T18:03:56Z","timestamp":1634580236000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219265921500122"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9]]},"references-count":25,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["10.1142\/S0219265921500122"],"URL":"https:\/\/doi.org\/10.1142\/s0219265921500122","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"type":"print","value":"0219-2659"},{"type":"electronic","value":"1793-6713"}],"subject":[],"published":{"date-parts":[[2021,9]]},"article-number":"2150012"}}