On friendly index sets of k-galaxies

S-M Lee (1304 N. First Avenue, Upland, CA 91786, USA)
Richard M. Low (Department of Mathematics, San Jose State University, San Jose, CA 95192, USA)
H.K. Ng (Department of Mathematics, San Jose State University, San Jose, CA 95192, USA)
Y-C Wang (Department of Digital Media Design, Tzu-Hui Institute of Technology, Taiwan, Republic of China)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 7, No 1 (2019): Electronic Journal of Graph Theory and Applications

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.