Full friendly index sets of cylinder graphs

Wai Chee SHIU, Fook Sun Wong

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

Let G = (V,E) be a connected simple graph. A labeling f: V → ℤ 2induces an edge labeling f +: E → ℤ 2 defined by f +(xy) = f(x) + f(y) for each xy ∈ E. For i ∈ ℤ 2, let v f(i) = {pipe}f -1(i){pipe} and e f(i) = {pipe}(f +) -1(i){pipe}. A labeling f is called friendly if {pipe}v f(1)-v f(0){pipe} ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by i f(G)=e f(1)-e f(0). The set {i f(G)f is a friendly labeling of G} is called the full friendly index set of G, denoted by FFI(G). In this paper, we determine the full friendly index sets of cylinder graphs C m × P n for even m ≥ 4, even n ≥ 4 and m ≤ 2n. We also list the results of other cases for m, n ≥ 4.

Original languageEnglish
Pages (from-to)141-162
Number of pages22
JournalAustralasian Journal of Combinatorics
Volume52
Publication statusPublished - Feb 2012

Scopus Subject Areas

  • Discrete Mathematics and Combinatorics

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