{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T22:57:53Z","timestamp":1762210673131},"reference-count":21,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2011,12]]},"abstract":"<jats:p>The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem and has recently been introduced by Park and Ihm.<jats:sup>15<\/jats:sup>In this paper, we examine properties of strong matching preclusion for alternating group graphs, by finding their strong matching preclusion numbers and categorizing all optimal solutions. More importantly, we prove a general result on taking a Cartesian product of a graph with K<jats:sub>2<\/jats:sub>(an edge) to obtain the corresponding results for split-stars.<\/jats:p>","DOI":"10.1142\/s0219265911003003","type":"journal-article","created":{"date-parts":[[2012,6,27]],"date-time":"2012-06-27T17:55:12Z","timestamp":1340819712000},"page":"277-298","source":"Crossref","is-referenced-by-count":25,"title":["STRONG MATCHING PRECLUSION FOR THE ALTERNATING GROUP GRAPHS AND SPLIT-STARS"],"prefix":"10.1142","volume":"12","author":[{"given":"PHILIP","family":"BONNEVILLE","sequence":"first","affiliation":[{"name":"Oakland University Summer Mathematics Institute, Oakland University, Rochester, MI 48309, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"EDDIE","family":"CHENG","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JOSEPH","family":"RENZI","sequence":"additional","affiliation":[{"name":"University Liggett School, 1045 Cook Road, Grosse Pointe Woods 48236, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,6,28]]},"reference":[{"key":"rf1","first-page":"185","volume":"174","author":"Brigham R. 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