{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T05:47:54Z","timestamp":1723096074619},"reference-count":0,"publisher":"Combinatorial Press","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p>Let \\(G=(V,E)\\) be a simple graph. A vertex \\(v\\in V(G)\\) ve-dominates every edge \\(uv\\) incident to \\(v\\), as well as every edge adjacent to these incident edges. A set \\(D\\subseteq V(G)\\) is a vertex-edge dominating set if every edge of \\(E(G)\\) is ve-dominated by a vertex of \\(D.\\) The MINIMUM VERTEX-EDGE DOMINATION problem is to find a vertex-edge dominating set of minimum cardinality. A linear time algorithm to find the minimum vertex-edge dominating set for proper interval graphs is proposed. The vertex-edge domination problem is proved to be APX-complete for bounded-free graphs and NP-Complete for Chordal bipartite and Undirected Path graphs.<\/jats:p>","DOI":"10.61091\/ars158-03","type":"journal-article","created":{"date-parts":[[2024,4,14]],"date-time":"2024-04-14T22:33:20Z","timestamp":1713134000000},"page":"19-26","source":"Crossref","is-referenced-by-count":0,"title":["Algorithmic Aspects of Vertex-edge Domination in Some Graphs"],"prefix":"10.61091","volume":"158","author":[{"name":"Department of Mathematics, School of Arts, Science, Humanities and Education, SASTRA Deemed University, Tanjore, India","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H Naresh","family":"Kumar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y B","family":"Venkatakrishnan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematics, School of Arts, Science, Humanities and Education, SASTRA Deemed University, Tanjore, India","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"39747","container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2024,4,14]],"date-time":"2024-04-14T22:33:25Z","timestamp":1713134005000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-158\/algorithmic-aspects-of-vertex-edge-domination-in-some-graphs\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1]]},"references-count":0,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2024,3,31]]},"published-print":{"date-parts":[[2024,3,31]]}},"URL":"https:\/\/doi.org\/10.61091\/ars158-03","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"type":"print","value":"0381-7032"},{"type":"electronic","value":"2817-5204"}],"subject":[],"published":{"date-parts":[[2024,1]]}}}