{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,23]],"date-time":"2025-03-23T04:21:40Z","timestamp":1742703700798,"version":"3.40.2"},"reference-count":0,"publisher":"Combinatorial Press","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2025,3,30]]},"abstract":"<jats:p>The degree of an edge \\(uv\\) of a graph \\(G\\) is \\(d_G(u)+d_G(v)-2.\\) The degree associated edge reconstruction number of a graph \\(G\\) (or dern(G)) is the minimum number of degree associated edge-deleted subgraphs that uniquely determines \\(G.\\) Graphs whose vertices all have one of two possible degrees \\(d\\) and \\(d+1\\) are called \\((d,d+1)\\)-bidegreed graphs. It was proved, in a sequence of two papers [1,17], that \\(dern(mK_{1,3})=4\\) for \\(m&gt;1,\\) \\(dern(mK_{2,3})=dern(rP_3)=3\\) for \\(m&gt;0, ~r&gt;1\\) and \\(dern(G)=1\\) or \\(2\\) for all other bidegreed graphs \\(G\\) except the \\((d,d+1)\\)-bidegreed graphs in which a vertex of degree \\(d+1\\) is adjacent to at least two vertices of degree \\(d.\\) In this paper, we prove that \\(dern(G)= 1\\) or \\(2\\) for this exceptional bidegreed graphs \\(G.\\) Thus, \\(dern(G)\\leq 4\\) for all bidegreed graphs \\(G.\\)<\/jats:p>","DOI":"10.61091\/ars162-02","type":"journal-article","created":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T16:54:46Z","timestamp":1742662486000},"page":"13-30","source":"Crossref","is-referenced-by-count":0,"title":["The degree associated edge reconstruction number of bidegreed graphs is at most four"],"prefix":"10.61091","volume":"162","author":[{"name":"Department of Mathematics, Vivekananda College, Agasteeswaram, Kanyakumari, Tamilnadu, India","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Anu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"Monikandan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematics, Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli, Tamilnadu, India","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"39747","published-online":{"date-parts":[[2025,3,30]]},"container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T16:54:49Z","timestamp":1742662489000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-162\/the-degree-associated-edge-reconstruction-number-of-bidegreed-graphs-is-at-most-four\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,30]]},"references-count":0,"URL":"https:\/\/doi.org\/10.61091\/ars162-02","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"value":"0381-7032","type":"print"},{"value":"2817-5204","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,30]]}}}