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graphs; adjacency matrix; eigenvalues of a graph; common neighbours
We find all connected graphs in which any two distinct vertices have exactly two common neighbors, thus solving a problem by B. Zelinka.
[1] D. Cvetković, M. Doob, H. Sachs: Spectra of Graphs. Theory and Applications. Johann A. Barth, Heidelberg, 1995. MR 1324340
[2] R. Diestel: Graph Theory. Second edition, Graduate Texts in Mathematics, vol. 173, Springer, New York, 2000. MR 1743598 | Zbl 0957.05001
[3] B. Zelinka: Graphs in which each pair of vertices has exactly two common neighbours. Math. Bohem. 118 (1993), 163–165. MR 1223481 | Zbl 0777.05092
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