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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Y-C Wang
Department of Digital Media Design, Tzu-Hui Institute of Technology, Taiwan, Republic of China
Electrical & Electronics Engineering

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On friendly index sets of k-galaxies S-M Lee; Richard M. Low; H.K. Ng; Y-C Wang
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 1 (2019): 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.2019.7.1.1

Abstract

Let G = (V, E) be a graph. A vertex labeling f : V → Z2 induces an edge labeling f *  : E → Z2 defined by f * (xy) = f(x) + f(y), for each edge xy ∈ E. For i ∈ Z2, let vf(i) = ∣{v ∈ V : f(v) = i}∣ and ef(i) = ∣{e ∈ E : f * (e) = i}∣. We say that f is friendly if ∣vf(1) − vf(0)∣ ≤ 1. The friendly index set of G, denoted by FI(G), is defined as FI(G) = ∣ef(1) − ef(0)∣ :  vertex labeling f is friendly. A k-galaxy is a disjoint union of k stars. In this paper, we establish the friendly index sets for various classes of k-galaxies.
Co-Authors H.K. Ng Richard M. Low S-M Lee