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Necessary and sufficient (just sufficient) conditions for the lower (upper) bound to be attained are deduced using edge clique partitions. As an application, we prove that the least eigenvalue of the <jats:italic>n<\/jats:italic>-Queens graph <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathcal {Q}}(n)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>Q<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is equal to <jats:inline-formula><jats:alternatives><jats:tex-math>$$-4$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mn>4<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> for every <jats:inline-formula><jats:alternatives><jats:tex-math>$$n \\ge 4$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>\u2265<\/mml:mo>\n                    <mml:mn>4<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and it is also proven that the multiplicity of this eigenvalue is <jats:inline-formula><jats:alternatives><jats:tex-math>$$(n-3)^2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mi>n<\/mml:mi>\n                      <mml:mo>-<\/mml:mo>\n                      <mml:mn>3<\/mml:mn>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Finally, edge clique partitions of additional infinite families of connected graphs and their relations with the least eigenvalues are presented.<\/jats:p>","DOI":"10.1007\/s10801-023-01247-1","type":"journal-article","created":{"date-parts":[[2023,6,13]],"date-time":"2023-06-13T11:02:29Z","timestamp":1686654149000},"page":"263-277","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions"],"prefix":"10.1007","volume":"58","author":[{"given":"Domingos M.","family":"Cardoso","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8511-9013","authenticated-orcid":false,"given":"In\u00eas Ser\u00f4dio","family":"Costa","sequence":"additional","affiliation":[]},{"given":"Rui","family":"Duarte","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,6,13]]},"reference":[{"issue":"1","key":"1247_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.disc.2007.12.043","volume":"309","author":"J Bell","year":"2009","unstructured":"Bell, J., Stevens, B.: A survey of known results and research areas for $$n$$-queens. 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