{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T05:46:50Z","timestamp":1723096010892},"reference-count":0,"publisher":"Combinatorial Press","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2023,12,31]]},"abstract":"<jats:p>A dominating broadcast of a graph G is a function f : V ( G ) \u2192 { 0 , 1 , 2 , \u2026 , diam ( G ) } such that f ( v ) \u2a7d e ( v ) for all v \u2208 V ( G ) , where e ( v ) is the eccentricity of v , and for every vertex u \u2208 V ( G ) , there exists a vertex v with f ( v ) &gt; 0 and d ( u , v ) \u2a7d f ( v ) . The cost of f is \u2211 v \u2208 V ( G ) f ( v ) . The minimum of costs over all the dominating broadcasts of G is called the broadcast domination number \u03b3 b ( G ) of G . A graph $G$ is said to be radial if \u03b3 b ( G ) = rad ( G ) . In this article, we give tight upper and lower bounds for the broadcast domination number of the line graph L ( G ) of G , in terms of \u03b3 b ( G ) , and improve the upper bound of the same for the line graphs of trees. We present a necessary and sufficient condition for radial line graphs of central trees, and exhibit constructions of infinitely many central trees T for which L ( T ) is radial. We give a characterization for radial line graphs of trees, and show that the line graphs of the i -subdivision graph of K 1 , n and a subclass of caterpillars are radial. Also, we show that \u03b3 b ( L ( C ) ) = \u03b3 ( L ( C ) ) for any caterpillar C .<\/jats:p>","DOI":"10.61091\/ars157-12","type":"journal-article","created":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T23:11:55Z","timestamp":1706051515000},"page":"121-131","source":"Crossref","is-referenced-by-count":0,"title":["Broadcast Domination in Line Graphs of Trees"],"prefix":"10.61091","volume":"157","author":[{"name":"Department of Mathematical and Computational Sciences National Institute of Technology Karnataka, Surathkal Mangalore \u2013 575025, India.","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jishnu","family":"Sen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Srinivasa Rao","family":"Kola","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematical and Computational Sciences National Institute of Technology Karnataka, Surathkal Mangalore \u2013 575025, India.","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"39747","published-online":{"date-parts":[[2023,12,31]]},"container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T23:12:15Z","timestamp":1706051535000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-157\/broadcast-domination-in-line-graphs-of-trees\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,31]]},"references-count":0,"URL":"https:\/\/doi.org\/10.61091\/ars157-12","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"type":"print","value":"0381-7032"},{"type":"electronic","value":"2817-5204"}],"subject":[],"published":{"date-parts":[[2023,12,31]]}}}