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MATHEMATICA BOHEMICA, Vol. 130, No. 1, pp. 101-105, 2005
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All graphs in which each pair of distinct vertices has exactly two common neighbors

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Dragan Stevanovic

* Dragan Stevanovic*, Faculty of Science and Mathematics, Visegradska 33, 18000 Nis, Serbia and Montenegro, e-mail: ` dragance@pmf.ni.ac.yu`

**Abstract:** We find all connected graphs in which any two distinct vertices have exactly two common neighbors, thus solving a problem by B. Zelinka.

**Keywords:** graphs, adjacency matrix, eigenvalues of a graph, common neighbours

**Classification (MSC 2000):** 05C75, 05C50

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