ℤ Halkası üzerinde nilpotent grafların laplasyan spektral özellikleri
birimli bir halka olsun. ' nin() ile gösterilen nilpotent grafı,()∗ = { ≠ ∈ :∈ ()≠∈ç } noktalar kümesi ve (), halkasının bütün nilpotent elemanlarının kümesi olmak üzere; “iki farklı venoktaları komşudur ⟺∈ ()” önermesini sağlayan kenarlar kümesinden oluşur. Bu makalede ℤ halkası üzerinde tanımlanan nilpotent grafın Laplasyan spektral özellikleri incelenmektedir.
Laplacian spectral properties of nilpotent graphs over ring ℤ
We consider a ring with unity. The nilpotent graph of is a graph with vertex set ()∗ = { ≠ ∈: ∈ ()≠ ∈ }; and two distinct vertices and are adjacent iff ∈ (),where () is the set of all nilpotent elements of and it is denoted by (). In this paper we studyLaplacian spectral properties of the nilpotent graph over the ring ℤ.
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