Sonlu devirli grupların birim grafları

Bu çalışmada sonlu devirli grupların birim grafları göz önüne alınmıştır. Sonlu devirli grupların birim grafları grupta tersi kendisi olan elemanların alt kümesi ve tersi kendisinden farklı elemanların alt kümesi ile ilişkili olarak incelenmiştir. Bu alt kümelerin özellikleri kullanılarak sonlu devirli grupların birim graflarındaki üçgen sayısı ve kenar sayısı belirlenmiştir. Ayrıca birim grafların Schultz, Gutman, birinci Zagreb, ikinci Zagreb ve Wiener indeksleri hesaplanmıştır.

Identity graphs of finite cyclic groups

In this paper, identity graphs of finite cyclic groups are considered. The identity graphs of finite cyclic groups are examined regarding to the subset of self-inverse elements and the subset of mutual inverse elements in a group. By using the features of these subsets the number of triangles and the number of edges in the identity graphs of finite cyclic groups are determined. Furthermore, Schultz, Gutman, first Zagreb, second Zagreb and Wiener indices are computed for identity graphs.

Keywords:

Graph, identity graph cyclic group, topological index,

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Anderson, D.F. and Livingston, P.S., The zero-divisor graph of a commutative ring, Journal of Algebra, 217: 434-447, (1999).
Anderson, D.F. and Badawi, A., The total graph of a commutative ring, Journal of Algebra, 320, 2706–2719, (2008).
Chalapathi, T. and Kumar, R.V.M.S.S., Invertible graphs of finite groups, Computer Science Journal of Moldova, 26(2), 126-145, (2018).
Dobrynin, A.A. and Kochetova, A.A., Degree Distance of a Graph: A degree analogue of the Wiener index, Journal of Chemical Information and Computer Sciences, 34, 1082-1086, (1994).
Gutman, I., and Trinajstic, N., Graph theory and molecular orbitals, Total φ-electron energy of alternant hydrocarbons, Chemical Physics Letters, 17, 535-538, (1972).
Gutman, I., Selected properties of the Schultz molecular topological index, Journal of Chemical Information and Computer Sciences, 34, 1087-1089, (1994).
Kandasamy, W.B.V. and Smarandache, F., Groups as Graphs, Editura CuArt 2009, http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm
Wiener, H., Structural determination of paraffin boiling points, Journal of the American Chemical Society, 69, 17-20, (1947).