Union of distance magic graphs

Cichacz, Sylwia; Nikodem, Mateusz

doi:10.7151/dmgt.1932

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A γ-Magic Rectangle Set Mrs γ (A B; C)1

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2018

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“…Kotzig arrays play an important role for graph labelings. There are many constructions based on Kotzig arrays of various magic-type constructions [3,4,9,13,14,16].…”

Section: A γ-Magic Rectangle Set Mrs γ (A B; C)mentioning

confidence: 99%

A magic rectangle set on Abelian groups

Cichacz,

Hinc

2018

Preprint

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A Γ-magic rectangle set M RS Γ (a, b; c) of order abc is a collection of c arrays (a × b) whose entries are elements of group Γ, each appearing once, with all row sums in every rectangle equal to a constant ω ∈ Γ and all column sums in every rectangle equal to a constant δ ∈ Γ.In this paper we prove that for {a, b} = {2 α , 2k + 1} where α and k are some natural numbers, a Γ-magic rectangle set MRS Γ (a, b; c) exists if and only if a and b are both even or and |Γ| is odd or Γ has more than one involution. Moreover we obtain sufficient and necessary conditions for existence a Γ-magic rectangle MRS Γ (a, b)=MRS Γ (a, b; 1).

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“…Kotzig arrays play an important role for graph labelings. There are many constructions based on Kotzig arrays of various magic-type constructions [3,4,9,13,14,16].…”

Section: A γ-Magic Rectangle Set Mrs γ (A B; C)mentioning

confidence: 99%