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All Journal Indonesian Journal of Combinatorics
Dalibor Froncek
University of Minnesota Duluth
Computer Science & IT Decision Sciences, Operations Research & Management

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Decomposition of complete graphs into connected unicyclic graphs with eight edges and pentagon Dalibor Froncek; O'Neill Kingston
Indonesian Journal of Combinatorics Vol 3, No 1 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (198.717 KB) | DOI: 10.19184/ijc.2019.3.1.3

Abstract

A G-decomposition of the complete graph Kn is a family of pairwise edge disjoint subgraphs of Kn, all isomorphic to G, such that every edge of Kn belongs to exactly one copy of G. Using standard decomposition techniques based on ρ-labelings, introduced by Rosa in 1967, and their modifications we show that each of the ten non-isomorphic connected unicyclic graphs with eight edges containing the pentagon decomposes the complete graph Kn whenever the necessary conditions are satisfied.
Z2nm-supermagic labeling of Cn#Cm Dalibor Froncek; James McKeown; John McKeown; Michael McKeown
Indonesian Journal of Combinatorics Vol 2, No 2 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (230.139 KB) | DOI: 10.19184/ijc.2018.2.2.1

Abstract

A Γ-supermagic labeling of a graph G = (V, E) with ∣E∣ = k is a bijection from E to an Abelian group Γ of order k such that the sum of labels of all incident edges of every vertex x ∈ V is equal to the same element μ ∈ Γ. We present a Z2nm-supermagic labeling of Cartesian product of two cycles, Cn□Cm for n odd. This along with an earlier result by Ivančo proves that a Z2nm-supermagic labeling of Cn□Cm exists for every n, m ≥ 3.
Γ-supermagic labeling of products of two cycles with cyclic groups Dalibor Froncek
Indonesian Journal of Combinatorics Vol 7, No 1 (2023)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2023.7.1.3

Abstract

A Γ-supermagic labeling of a graph G=(V,E) is a bijection from E to a group Γ of order |E| such that the sum of labels of all edges incident with any vertex x∈ V is equal to the same element μ ∈ Γ. A Z2mn-supermagic labeling of the Cartesian product of two cycles, Cm ℺ Cn for every m,n ≥ 3 was found by Froncek, McKeown, McKeown, and McKeown. In this paper we present a Zk-supermagic labeling of the direct and strong product by cyclic group Zk for any m,n ≥ 3.
Co-Authors James McKeown John McKeown Michael McKeown O'Neill Kingston