Identity graphs of finite cyclic groups

Year 2020, Volume: 22 Issue: 1, 149 - 158, 10.01.2020

Nazmiye Feyza Yalçın Yakup Kırğıl

https://doi.org/10.25092/baunfbed.679578

Abstract

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

Sonlu devirli grupların birim grafları

Abstract

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.

Keywords

Graf , birim graf , devirli grup , topolojik indeks

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