Abstract
The sum of positive eigenvalues and the number of the edges of a graphG are denoted byS(G) and #E(G) respectively. C. Delorme[1] put forward the question: What is the lower bound ofS(G) for a given #E(G)? Is it\(\sqrt {\# E(G)} \)? In this paper we give an affirmative answer to the question.
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C. Delorme. Decomposition into Complete Bipartite Graphs and Quadratic forms. In Proceedings of Codigraf'93 Conference, held at La Platja d'Aro (Catalunya), Sept. 22–24, 1993, Universitat Autónoma de Barcelona, Barcelona, 1993, pp. 145–154.
R. Brualdi and H.J. Ryser. Combinatorial Matrix Theory. Cambridge University Press, London, 1991.
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This work is supported by the Natural National Science Foundation of China, Grant No. 19671077
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Jiongsheng, L., Xinmao, W. Lower bound of the sum of positive eigenvalues of a graph. Acta Mathematicae Applicatae Sinica 14, 443–446 (1998). https://doi.org/10.1007/BF02683829
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DOI: https://doi.org/10.1007/BF02683829