On irregularities in the graph of generalized divisor functions

Gergely Zábrádi

Displaying similar documents to “On irregularities in the graph of generalized divisor functions”

Characterizing which Powers of Hypercubes and Folded Hyper- cubes Are Divisor Graphs

Eman A. AbuHijleh, Omar A. AbuGhneim, Hasan Al-Ezeh (2015)

Discussiones Mathematicae Graph Theory

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In this paper, we show that Qkn is a divisor graph, for n = 2, 3. For n ≥ 4, we show that Qkn is a divisor graph iff k ≥ n − 1. For folded-hypercube, we get FQn is a divisor graph when n is odd. But, if n ≥ 4 is even integer, then FQn is not a divisor graph. For n ≥ 5, we show that (FQn)k is not a divisor graph, where 2 ≤ k ≤ [n/2] − 1.

Some properties of the zero divisor graph of a commutative ring

Khalida Nazzal, Manal Ghanem (2014)

Discussiones Mathematicae - General Algebra and Applications

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Let Γ(R) be the zero divisor graph for a commutative ring with identity. The k-domination number and the 2-packing number of Γ(R), where R is an Artinian ring, are computed. k-dominating sets and 2-packing sets for the zero divisor graph of the ring of Gaussian integers modulo n, Γ(ℤₙ[i]), are constructed. The center, the median, the core, as well as the automorphism group of Γ(ℤₙ[i]) are determined. Perfect zero divisor graphs Γ(R) are investigated.

Cesàro means related to the square of the divisor function

Gintautas Bareikis, Algirdas Mačiulis (2012)

Acta Arithmetica

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The range of the sum-of-proper-divisors function

Florian Luca, Carl Pomerance (2015)

Acta Arithmetica

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Answering a question of Erdős, we show that a positive proportion of even numbers are in the form s(n), where s(n) = σ(n) - n, the sum of proper divisors of n.