{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T18:05:56Z","timestamp":1771956356491,"version":"3.50.1"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,12]]},"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 [Formula: see text] of [Formula: see text] is the minimum cardinality taken over all dominating sets of [Formula: see text]. The shadow graph of [Formula: see text], denoted [Formula: see text] is the graph constructed from [Formula: see text] by taking two copies of [Formula: see text] namely [Formula: see text] itself and [Formula: see text] and by joining each vertex [Formula: see text] in [Formula: see text] to the neighbors of the corresponding vertex [Formula: see text] in [Formula: see text]. In this paper, we obtain the upper and lower bounds for the sum of domination number of a graph and its shadow graph and characterize such extremal graphs. <\/jats:p>","DOI":"10.1142\/s1793830921500749","type":"journal-article","created":{"date-parts":[[2020,12,14]],"date-time":"2020-12-14T07:15:10Z","timestamp":1607930110000},"source":"Crossref","is-referenced-by-count":3,"title":["On the domination number of a graph and its shadow graph"],"prefix":"10.1142","volume":"13","author":[{"given":"E.","family":"Murugan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli \u2013 627 012, Tamil Nadu, India"}]},{"given":"G. 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