On Unicyclic Graphs Spectra : New Results

Abstract : Let G = (V, E) be a unicyclic simple undirected graph. In this paper, we investigate the spectra of a particular class of unicyclic graphs G(q, n1) where q is the size of the unique cycle. Each vertex of the unique cycle is attached to n1 vertices. We provide the " exact values " of the extremal eigenvalues of the adjacency matrix A and the Laplacian matrix L of G, in contrast to lower and upper bounds reported in the literature.
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DCABES 2016 (15th International Symposium on Distributed Computing and Applications to Business, Engineering and Science), Aug 2016, Paris, France. IEEE, pp.586-593, 2017, 2016 IEEE Intl Conference on Computational Science and Engineering (CSE) and IEEE Intl Conference on Embedded and Ubiquitous Computing (EUC) and 15th Intl Symposium on Distributed Computing and Applications for Business Engineering (DCABES). 〈http://ieeexplore.ieee.org/Xplore/home.jsp〉. 〈10.1109/CSE-EUC-DCABES.2016.245〉
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Makhlouf Hadji, Ming Chau. On Unicyclic Graphs Spectra : New Results. DCABES 2016 (15th International Symposium on Distributed Computing and Applications to Business, Engineering and Science), Aug 2016, Paris, France. IEEE, pp.586-593, 2017, 2016 IEEE Intl Conference on Computational Science and Engineering (CSE) and IEEE Intl Conference on Embedded and Ubiquitous Computing (EUC) and 15th Intl Symposium on Distributed Computing and Applications for Business Engineering (DCABES). 〈http://ieeexplore.ieee.org/Xplore/home.jsp〉. 〈10.1109/CSE-EUC-DCABES.2016.245〉. 〈hal-01427303〉

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