{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T12:56:44Z","timestamp":1648990604265},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2010,6]]},"abstract":"<jats:p> A vertex subset S of a graph G = (V, E) is a double dominating set for G if |N[v]\u2229S| \u2265 2 for each vertex v \u2208 V, where N[v] = {u |uv \u2208 E}\u222a{v}. The double domination number of G, denoted by \u03b3<jats:sub>\u00d72<\/jats:sub>(G), is the cardinality of a smallest double dominating set of G. A graph G is said to be double domination edge critical if \u03b3<jats:sub>\u00d72<\/jats:sub>(G + e) &lt; \u03b3<jats:sub>\u00d72<\/jats:sub>(G) for any edge e \u2209 E. A double domination edge critical graph G with \u03b3<jats:sub>\u00d72<\/jats:sub>(G) = k is called k - \u03b3<jats:sub>\u00d72<\/jats:sub>(G)-critical. In this paper, we first show that G has a perfect matching if G is a connected 3 - \u03b3<jats:sub>\u00d72<\/jats:sub>(G)-critical graph of even order. Secondly, we show that G is factor-critical if G is a connected 3 - \u03b3<jats:sub>\u00d72<\/jats:sub>(G)-critical graph with odd order and minimum degree at least 2. Finally, we show that G is factor-critical if G is a connected K<jats:sub>1,4<\/jats:sub>-free 4 - <jats:sub>\u03b3\u00d72<\/jats:sub>(G)-critical graph of odd order with minimum degree at least 2. <\/jats:p>","DOI":"10.1142\/s1793830910000541","type":"journal-article","created":{"date-parts":[[2010,7,5]],"date-time":"2010-07-05T10:31:23Z","timestamp":1278325883000},"page":"151-160","source":"Crossref","is-referenced-by-count":1,"title":["MATCHING PROPERTIES IN DOUBLE DOMINATION EDGE CRITICAL GRAPHS"],"prefix":"10.1142","volume":"02","author":[{"given":"HAICHAO","family":"WANG","sequence":"first","affiliation":[{"name":"Department of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LIYING","family":"KANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai University, Shanghai 200444, P. R. 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