{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:54Z","timestamp":1740134574311,"version":"3.37.3"},"reference-count":20,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11371109"],"award-info":[{"award-number":["11371109"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["11371109"],"award-info":[{"award-number":["11371109"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Let<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>W<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>n<\/mml:mi><mml:mo>;<\/mml:mo><mml:mi>q<\/mml:mi><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>be the unicyclic graph with<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>vertices obtained by attaching two paths of lengths<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>at two adjacent vertices of cycle<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>q<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>. Let<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mi>U<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>n<\/mml:mi><mml:mo>;<\/mml:mo><mml:mi>q<\/mml:mi><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>,<\/mml:mo><mml:mo>\u2026<\/mml:mo><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>s<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>be the unicyclic graph with<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>vertices obtained by attaching<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:mi>s<\/mml:mi><\/mml:mrow><\/mml:math>paths of lengths<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>,<\/mml:mo><mml:mo>\u2026<\/mml:mo><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>s<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:math>at the same vertex of cycle<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>q<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>. In this paper, we prove that<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mi>W<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>n<\/mml:mi><mml:mo>;<\/mml:mo><mml:mi>q<\/mml:mi><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mi>U<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>n<\/mml:mi><mml:mo>;<\/mml:mo><mml:mi>q<\/mml:mi><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>,<\/mml:mo><mml:mo>\u2026<\/mml:mo><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>m<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>s<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>are determined by their Laplacian spectra when<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\"><mml:mrow><mml:mi>q<\/mml:mi><\/mml:mrow><\/mml:math>is even.<\/jats:p>","DOI":"10.1155\/2014\/268464","type":"journal-article","created":{"date-parts":[[2014,9,3]],"date-time":"2014-09-03T23:40:05Z","timestamp":1409787605000},"page":"1-6","source":"Crossref","is-referenced-by-count":0,"title":["Laplacian Spectral Characterization of Some Unicyclic Graphs"],"prefix":"10.1155","volume":"2014","author":[{"given":"Lijun","family":"Yu","sequence":"first","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, 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