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Math."],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    A vertex set in a graph without isolated vertices is a total restrained dominating set (TRD-set) if it is dominating, induces a subgraph without isolated vertices, and the vertices not in the set also induce a subgraph without isolated vertices. Two vertex sets, which are not TRD-sets, form a total restrained coalition if their union is a TRD-set. A total restrained coalition partition is a partition where none of its elements are TRD-sets, but each forms a total restrained coalition with another element. The goal is to maximize the cardinality of such a partition, denoted\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$C_{tr}(G)$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>C<\/mml:mi>\n                              <mml:mrow>\n                                <mml:mi>tr<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:mrow>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mi>G<\/mml:mi>\n                              <mml:mo>)<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . We initiate the study of this concept by proving certain properties, extremal values, general bounds, and its relation to known structural parameters. Exact values for specific graph families are also provided.\n                  <\/jats:p>","DOI":"10.1007\/s40314-025-03439-w","type":"journal-article","created":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T05:19:31Z","timestamp":1760505571000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Total restrained coalitions in graphs"],"prefix":"10.1007","volume":"45","author":[{"given":"M.","family":"Chellali","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.","family":"Golmohammadi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N. A.","family":"Matrokhin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"I. I.","family":"Takhonov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6830-492X","authenticated-orcid":false,"given":"J. C.","family":"Valenzuela-Tripodoro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,10,15]]},"reference":[{"issue":"11","key":"3439_CR1","doi-asserted-by":"publisher","first-page":"2283","DOI":"10.2989\/16073606.2024.2365365","volume":"47","author":"S Alikhani","year":"2024","unstructured":"Alikhani S, Bakhshesh D, Golmohammadi H (2024a) Total coalitions in graphs. 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