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On Integral Graphs with Few Cycles

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Abstract

A graph is called integral if the spectrum of its adjacency matrix has only integer eigenvalues. In this paper, all integral graphs with at most two cycles (trees, unicyclic and bicyclic graphs) with no eigenvalue 0 are identified. Moreover, we give some results on unicyclic integral graphs with exactly one eigenvalue 0.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran

    G. R. Omidi

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran

    G. R. Omidi

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  1. G. R. Omidi
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Correspondence to G. R. Omidi.

Additional information

This research was in part supported by a grant from IPM (No. 88050012).

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Omidi, G.R. On Integral Graphs with Few Cycles. Graphs and Combinatorics 25, 841–849 (2009). https://doi.org/10.1007/s00373-010-0913-1

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  • DOI: https://doi.org/10.1007/s00373-010-0913-1

Keywords

Mathematics Subject Classification (2000)