{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T05:46:39Z","timestamp":1723095999127},"reference-count":0,"publisher":"Combinatorial Press","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2023,7,31]]},"abstract":"<jats:p>For a graph \\(G\\) and a positive integer \\(k\\),  a royal \\(k\\)-edge coloring of \\(G\\) is an assignment of nonempty subsets of the set \\(\\{1, 2, \\ldots, k\\}\\)  to the edges of \\(G\\) that gives rise to a proper vertex coloring in which the color assigned to each vertex \\(v\\) is the union of the sets of colors of  the edges incident with \\(v\\). If the resulting vertex coloring is  vertex-distinguishing, then  the edge coloring is   a   strong  royal  \\(k\\)-coloring.  The minimum positive integer \\(k\\) for which a graph   has a strong royal \\(k\\)-coloring is the   strong royal index  of the graph.   The primary  emphasis  here is on  strong royal colorings of trees.<\/jats:p>","DOI":"10.61091\/ars156-06","type":"journal-article","created":{"date-parts":[[2023,8,5]],"date-time":"2023-08-05T05:53:09Z","timestamp":1691214789000},"page":"51-63","source":"Crossref","is-referenced-by-count":0,"title":["Royal Colorings of Graphs"],"prefix":"10.61091","volume":"156","author":[{"name":"Department of Mathematics Western Michigan University Kalamazoo, MI 49008, USA","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gary","family":"Chartrand","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James","family":"Hallas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematics Western Michigan University Kalamazoo, MI 49008, USA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ping","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematics Western Michigan University Kalamazoo, MI 49008, USA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"39747","published-online":{"date-parts":[[2023,7,31]]},"container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2023,8,5]],"date-time":"2023-08-05T05:53:10Z","timestamp":1691214790000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatoire.com\/ars\/article\/Royal-Colorings-of-Graphs.pdf"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,31]]},"references-count":0,"URL":"https:\/\/doi.org\/10.61091\/ars156-06","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"type":"print","value":"0381-7032"},{"type":"electronic","value":"2817-5204"}],"subject":[],"published":{"date-parts":[[2023,7,31]]}}}