{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T14:11:29Z","timestamp":1767708689740,"version":"3.48.0"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Port. Math."],"accepted":{"date-parts":[[2025,11,27]]},"published-print":{"date-parts":[[2026,1,6]]},"abstract":"<jats:p>\n                    Let\n                    <jats:inline-formula>\n                      <jats:tex-math>G<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    be a simple graph and\n                    <jats:inline-formula>\n                      <jats:tex-math>k\\in\\mathbb{N}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . Two important graph operations are: the\n                    <jats:inline-formula>\n                      <jats:tex-math>k<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -th graph power of\n                    <jats:inline-formula>\n                      <jats:tex-math>G<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , denoted by\n                    <jats:inline-formula>\n                      <jats:tex-math>G^{k}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , where\n                    <jats:inline-formula>\n                      <jats:tex-math>G^{k}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is the graph obtained from\n                    <jats:inline-formula>\n                      <jats:tex-math>G<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    by adding an edge between every pair of vertices that have a distance at most\n                    <jats:inline-formula>\n                      <jats:tex-math>k<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , and the complement graph of\n                    <jats:inline-formula>\n                      <jats:tex-math>G<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , denoted by\n                    <jats:inline-formula>\n                      <jats:tex-math>\\overline{G}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . In this paper, we studied the relation between the independence numbers of\n                    <jats:inline-formula>\n                      <jats:tex-math>\\overline{G}^{k}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and\n                    <jats:inline-formula>\n                      <jats:tex-math>\\overline{G^k}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    .\n                  <\/jats:p>","DOI":"10.4171\/pm\/2158","type":"journal-article","created":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T14:09:11Z","timestamp":1767708551000},"source":"Crossref","is-referenced-by-count":0,"title":["Evaluating a permutation of the power and complement operations of a graph with respect to its independence numbers"],"prefix":"10.4171","author":[{"given":"Margarida","family":"Cleto","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02xankh89","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade Nova de Lisboa, Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2695-9079","authenticated-orcid":false,"given":"Ros\u00e1rio","family":"Fernandes","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02xankh89","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade Nova de Lisboa, Caparica, Portugal"}]},{"given":"R\u00faben","family":"Palma","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02xankh89","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade Nova de Lisboa, Caparica, Portugal"}]}],"member":"2673","container-title":["Portugaliae Mathematica"],"original-title":[],"deposited":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T14:09:11Z","timestamp":1767708551000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/pm\/2158"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,6]]},"references-count":0,"URL":"https:\/\/doi.org\/10.4171\/pm\/2158","relation":{},"ISSN":["0032-5155","1662-2758"],"issn-type":[{"value":"0032-5155","type":"print"},{"value":"1662-2758","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,6]]}}}