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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Aaron Shepanik
Department of Mathematics and Statistics, University of Minnesota Duluth Duluth, USA
Electrical & Electronics Engineering

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On regular handicap graphs of order $n \equiv 0$ mod 8 Dalibor Froncek; Aaron Shepanik
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 2 (2018): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2018.6.2.1

Abstract

A handicap distance antimagic labeling of a graph G = (V, E) with n vertices is a bijection f̂ : V → {1, 2, …, n} with the property that f̂(xi) = i, the weight w(xi) is the sum of labels of all neighbors of xi, and the sequence of the weights w(x1), w(x2), …, w(xn) forms an increasing arithmetic progression. A graph G is a handicap distance antimagic graph if it allows a handicap distance antimagic labeling. We construct r-regular handicap distance antimagic graphs of order $n \equiv 0 \pmod{8}$ for all feasible values of r.
Co-Authors Dalibor Froncek