{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:21:13Z","timestamp":1753885273554,"version":"3.41.2"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2022,10]]},"abstract":"<jats:p> Let [Formula: see text] be a graph. A subset [Formula: see text] of [Formula: see text] is called a dominating set of [Formula: see text] if every vertex not in [Formula: see text] is adjacent to some vertex in [Formula: see text] The domination number\u00a0[Formula: see text] of [Formula: see text] is the minimum cardinality taken over all dominating sets of [Formula: see text] The block graph\u00a0[Formula: see text] of a graph [Formula: see text] is a graph whose vertex set is the set of blocks in [Formula: see text] and two vertices of [Formula: see text] are adjacent if and only if the corresponding blocks have a common cut vertex in [Formula: see text] In this paper, we investigate the lower and upper bounds for the sum of domination number of a graph and its block graph and characterize the extremal graphs. <\/jats:p>","DOI":"10.1142\/s1793830922500331","type":"journal-article","created":{"date-parts":[[2021,10,5]],"date-time":"2021-10-05T02:27:07Z","timestamp":1633400827000},"source":"Crossref","is-referenced-by-count":1,"title":["On the domination number of a graph and its block graph"],"prefix":"10.1142","volume":"14","author":[{"given":"E.","family":"Murugan","sequence":"first","affiliation":[{"name":"Department of Mathematics, C. S. I Jayaraj Annapackiam College, Nallur 627 853, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Paulraj Joseph","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627 012, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,11,27]]},"reference":[{"key":"S1793830922500331BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2011.12.018"},{"key":"S1793830922500331BIB002","doi-asserted-by":"publisher","DOI":"10.11650\/twjm\/1500406930"},{"volume-title":"Theory of Graphs and its Applications","year":"1962","author":"Berge C.","key":"S1793830922500331BIB003"},{"key":"S1793830922500331BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830913500183"},{"key":"S1793830922500331BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-970-5"},{"key":"S1793830922500331BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(99)00251-4"},{"key":"S1793830922500331BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF01848079"},{"key":"S1793830922500331BIB008","first-page":"728","volume":"274","author":"Jaeger F.","year":"1972","journal-title":"C. R. Acad. Sci. Paris Ser. A"},{"key":"S1793830922500331BIB009","first-page":"489","volume":"19","author":"Mitchell S.","year":"1977","journal-title":"Congr. Numer."},{"issue":"4","key":"S1793830922500331BIB010","first-page":"222","volume":"6","author":"Murugan E.","year":"2019","journal-title":"Global J. Eng. Sci. Res."},{"issue":"1","key":"S1793830922500331BIB011","first-page":"170","author":"Murugan E.","year":"2018","journal-title":"Int. J. Math. Combin."},{"key":"S1793830922500331BIB012","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830920500688"},{"key":"S1793830922500331BIB013","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830920500688"},{"key":"S1793830922500331BIB014","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548300002042"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830922500331","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,15]],"date-time":"2022-10-15T03:48:28Z","timestamp":1665805708000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830922500331"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,27]]},"references-count":14,"journal-issue":{"issue":"07","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["10.1142\/S1793830922500331"],"URL":"https:\/\/doi.org\/10.1142\/s1793830922500331","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2021,11,27]]},"article-number":"2250033"}}