On analogues of nilpotent and total graphs associated ring $\mathbb{Z}_n$

Year 2023, Volume: 2 Issue: 1, 1 - 4, 30.06.2023

Hatice Pınar Cantekin , Sezer Sorgun

Abstract

In the last 20 years, the graphs associated with a ring have been introduced, such as the zero-divisor graph, the nilpotent graph, the total graph, etc. The studies on these graphs are generally related to their graph invariants. In this paper, we define two novel analogue graphs over the integer rings and obtain some properties as well as the spectrum with respect to the adjacency matrix.

Keywords

Graph, Nilpotent Graph, spectrum

$\mathbb{Z}_n$ halkası üzerinde tanımlı nilpotent ve total grafların analogları üzerine

Abstract

Son 20 yıldır, sıfır bölen çizge, nilpotent çizge ve total çizge gibi bir halkadan oluşmuş çizgeler tanıtılmıştır. Bu çizgeler üzerinde yapılan çalışmalar genellikle .çizge değişmezleri üzerinedir. Bu makalede nilpotent ve total çizgelerden yardımıyla Z_n tam sayı halkasında iki yeni benzer çizge tanımı yapılmıştır ve bu çizgelerin komşuluk spektrumları yanı sıra bazı özellikleri der verilmiştir.

Keywords

Graph, Nilpotent Graph, Total Graph, spectrum

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