Integral graphs;
Complete matchings;
Bipartite graphs;
05C50;
D O I:
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摘要:
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.