| Institution: | aDepartment of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China;bCollege of Computer and Educational Software, Guangzhou University, Guangzhou 510006, China;cDepartment of Mathematics, University of Puerto Rico at Mayaguez, P.O. Box 9018, PR 00681, USA |
| Abstract: | Let H(n;q,n1,n2) be a graph with n vertices containing a cycle Cq and two hanging paths Pn1 and Pn2 attached at the same vertex of the cycle. In this paper, we prove that except for the A-cospectral graphs H(12;6,1,5) and H(12;8,2,2), no two non-isomorphic graphs of the form H(n;q,n1,n2) are A-cospectral. It is proved that all graphs H(n;q,n1,n2) are determined by their L-spectra. And all graphs H(n;q,n1,n2) are proved to be determined by their Q-spectra, except for graphs  with a being a positive even number and  with b≥4 being an even number. Moreover, the Q-cospectral graphs with these two exceptions are given. |
