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The dumbbell graph, denoted by [Formula: see text], is the graph obtained from two cycles [Formula: see text], [Formula: see text] and a path [Formula: see text] by identifying each pendant vertex of [Formula: see text] with a vertex of a cycle, respectively. The theta graph, denoted by [Formula: see text], is the graph formed by joining two given vertices via three disjoint paths [Formula: see text], [Formula: see text] and [Formula: see text], respectively. In this paper, we prove that all dumbbell graphs as well as all theta graphs are determined by their [Formula: see text]-spectra.<\/jats:p>","DOI":"10.1142\/s1793830916500282","type":"journal-article","created":{"date-parts":[[2016,2,18]],"date-time":"2016-02-18T10:28:32Z","timestamp":1455791312000},"page":"1650028","source":"Crossref","is-referenced-by-count":4,"title":["Laplacian spectral characterization of dumbbell graphs and theta graphs"],"prefix":"10.1142","volume":"08","author":[{"given":"Xiaogang","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an 710072, Shaanxi, P. R. 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