Full friendly index sets of P2 × Pn

Wai Chee SHIU; Harris Kwong

doi:10.1016/j.disc.2007.07.002

Full friendly index sets of P₂ × P_n

Wai Chee SHIU^*, Harris Kwong

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

24 Citations (Scopus)

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 xy ∈ E. For each i ∈ Z₂, define v_f (i) = | f^{- 1} (i) | and e_f (i) = | f^{*- 1} (i) |. We call f friendly if | v_f (1) - v_f (0) | ≤ 1. The full friendly index set of G is the set of all possible values of e_f (1) - e_f (0), where f is friendly. In this note, we study the full friendly index set of the grid graph P₂ × P_n.

Original language	English
Pages (from-to)	3688-3693
Number of pages	6
Journal	Discrete Mathematics
Volume	308
Issue number	16
DOIs	https://doi.org/10.1016/j.disc.2007.07.002
Publication status	Published - 28 Aug 2008

Scopus Subject Areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

User-Defined Keywords

Friendly index
Grid

Access to Document

10.1016/j.disc.2007.07.002

Cite this

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title = "Full friendly index sets of P2 × Pn",

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 xy ∈ E. For each i ∈ Z2, define vf (i) = | f- 1 (i) | and ef (i) = | f*- 1 (i) |. We call f friendly if | vf (1) - vf (0) | ≤ 1. The full friendly index set of G is the set of all possible values of ef (1) - ef (0), where f is friendly. In this note, we study the full friendly index set of the grid graph P2 × Pn.",

keywords = "Friendly index, Grid",

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note = "Funding Information: This work is supported by FRG, Hong Kong Baptist University. ",

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AU - SHIU, Wai Chee

AU - Kwong, Harris

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PY - 2008/8/28

Y1 - 2008/8/28

N2 - 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 xy ∈ E. For each i ∈ Z2, define vf (i) = | f- 1 (i) | and ef (i) = | f*- 1 (i) |. We call f friendly if | vf (1) - vf (0) | ≤ 1. The full friendly index set of G is the set of all possible values of ef (1) - ef (0), where f is friendly. In this note, we study the full friendly index set of the grid graph P2 × Pn.

AB - 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 xy ∈ E. For each i ∈ Z2, define vf (i) = | f- 1 (i) | and ef (i) = | f*- 1 (i) |. We call f friendly if | vf (1) - vf (0) | ≤ 1. The full friendly index set of G is the set of all possible values of ef (1) - ef (0), where f is friendly. In this note, we study the full friendly index set of the grid graph P2 × Pn.

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