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Article

Stevanović, Dragan
All graphs in which each pair of distinct vertices has exactly two common neighbors. (English). Mathematica Bohemica, vol. 130 (2005), issue 1, pp. 101-105
MSC: 05C50, 05C75 | MR 2128363 | Zbl 1110.05064 | DOI: 10.21136/MB.2005.134219
Keywords:
graphs; adjacency matrix; eigenvalues of a graph; common neighbours
Summary:
We find all connected graphs in which any two distinct vertices have exactly two common neighbors, thus solving a problem by B. Zelinka.
References:
[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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