On friendly index sets of k-galaxies

S-M Lee, Richard M. Low, H.K. Ng, Y-C Wang

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.


Keywords


friendly labeling, friendly index set, disjoint union of stars

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DOI: http://dx.doi.org/10.5614/ejgta.2019.7.1.1

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