{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T22:31:10Z","timestamp":1726439470121},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,6]]},"abstract":"<jats:p> Let [Formula: see text] be a graph of order [Formula: see text] and size [Formula: see text] A dominating set [Formula: see text] of [Formula: see text] is called a secure dominating set if for each [Formula: see text] there exists [Formula: see text] such that [Formula: see text] is adjacent to [Formula: see text] and [Formula: see text] is a dominating set of [Formula: see text] In this case, we say that [Formula: see text] is [Formula: see text]-defended by [Formula: see text] or [Formula: see text] [Formula: see text]-defends [Formula: see text] The secure domination number [Formula: see text] is the minimum cardinality of a secure dominating set of [Formula: see text] The secure domination subdivision number of [Formula: see text] is the minimum number of edges that must be subdivided (each edge in [Formula: see text] can be subdivided at most once) in order to increase the secure domination number. In this paper, we present several results on this parameter. <\/jats:p>","DOI":"10.1142\/s1793830919500368","type":"journal-article","created":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T03:08:46Z","timestamp":1557457726000},"page":"1950036","source":"Crossref","is-referenced-by-count":1,"title":["Secure domination subdivision number of a graph"],"prefix":"10.1142","volume":"11","author":[{"given":"S. V.","family":"Divya Rashmi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Vidyavardhaka College of Engineering, Mysuru 570002, Karnataka, India"}]},{"given":"A.","family":"Somasundaram","sequence":"additional","affiliation":[{"name":"Department of Mathematics, BITS, Pilani-Dubai, Dubai International Academic City, UAE"}]},{"given":"S.","family":"Arumugam","sequence":"additional","affiliation":[{"name":"National Centre for Advanced Research in Discrete Mathematics, Kalasalingam University, Anand Nagar, Krishnankoil 626 126, Tamil Nadu, India"},{"name":"Department of Computer Science, Liverpool Hope University, Liverpool, UK Department of Computer Science, Ball State University, USA"}]}],"member":"219","published-online":{"date-parts":[[2019,7,9]]},"reference":[{"key":"S1793830919500368BIB001","first-page":"41","volume-title":"in Proc. the Conf. on Graph connections","author":"Arumugam S.","year":"1999"},{"key":"S1793830919500368BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s00010-009-2981-y"},{"key":"S1793830919500368BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90085-7"},{"issue":"105","key":"S1793830919500368BIB004","first-page":"5203","volume":"8","author":"Castillano E. 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