A note on the spectral characterization of dumbbell graphs |
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Authors: | Jianfeng Wang Qiongxiang Huang Francesco Belardo Enzo M. Li Marzi |
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Affiliation: | aCollege of Mathematics and System Science, Xinjiang University, Urumqi 830046, PR China;bDepartment of Mathematics, Qinghai Normal University, Xining, Qinghai 810008, PR China;cDepartment of Mathematics, University of Messina, 98166 Sant’Agata, Messina, Italy |
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Abstract: | The dumbbell graph, denoted by Da,b,c, is a bicyclic graph consisting of two vertex-disjoint cycles Ca and Cb joined by a path Pc+3 (c-1) having only its end-vertices in common with the two cycles. By using a new cospectral invariant for (r,r+1)-almost regular graphs, we will show that almost all dumbbell graphs (without cycle C4 as a subgraph) are determined by the adjacency spectrum. |
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Keywords: | Spectrum Spectral radius Cospectral graphs Almost regular graphs |
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