Geodesic
The finite-dimensional analog of Laplace operator on the graph
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 39 (2012) no. 1, pp. 95-96.

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The finite-difference analogs of the one-dimensional Laplace operator on the graph, representing the chain of stars, is considered. The received finite-dimensional operator inherits based properties of the Laplace operator, such as symmetry and positivity.
Keywords: graph–chain of stars, the Laplace operator on the graph, finite-difference analog of Laplace operator. 
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O. A. Makhinova. The finite-dimensional analog of Laplace operator on the graph. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 39 (2012) no. 1, pp. 95-96. http://geodesic.mathdoc.fr/item/IIMI_2012_39_1_a44/

[1] Marchuk G.I., Metody vychislitelnoi matematiki, Nauka, M., 1977, 455 pp.

[2] Makhinova O.A., “Zadacha teploperenosa na grafakh s tsiklom”, Sistemy upravleniya i informatsionnye tekhnologii, 2010, no. 1(39), 19–22

[3] Makhinova O.A., “Approksimatsiya odnomernogo operatora Laplasa na grafe-zvezde”, Vestnik Tambovskogo Gosudarstvennogo universiteta, 16:4 (2011), 1124–1126