Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

LetG = (V,E) be a connected graph without loops. A vertex labeling g : V [arrow right] Z^sub 2^ induces two edge labelings f^sup +^, f* : E [arrow right] Z^sub 2^, given by f^sup +^(uv) = f(u) + f(v) and f*(uv) = f(u)f(v) for each uv ∈ E respectively. For j ∈ Z^sub 2^, let v^sub f^ (j) = |f^sup -1^(j)|, e^sub f+^(j) = |(f^sup +^)^sup -1^(j)| and e^sub f*^ (j) = |(f*)^sup -1^(j)|. A vertex labeling f is called friendly if |v^sub f^ (1) - v^sub f^ (0)| ≤ 1. For a friendly labeling f of G, the friendly index of G with respect to f is defined to be i^sup +^^sub f^ (G) = e^sup +^^sub f+^(1) - e^sub f+^(0), and the product-cordial index is defined to be i*^sub f^ (G) = e^sub f*^(1) - e^sub f*^(0). The full friendly index set (FFI) and the full product-cordial index set (FPCI) of G contain precisely all the values i^sup +^^sub f^ (G) and i*^sub f^ (G) taken over all friendly labelings of G, respectively. In this paper, we study the FFI and the FPCI of odd twisted cylinder and two permutation Petersen graphs.

Keywords

Full friendly indexsets, full product-cordial index sets, permutationPetersen graph

Publication Date

2013

Source Publication Title

Journal of Combinatorics and Number Theory

Volume

5

Issue

3

Start Page

227

End Page

244

Publisher

Nova Science Publishers

Peer Reviewed

1

Copyright

© NovaSciencePublishers, Inc.

Funder

This work is partially supported by the Faculty Research Grant, Hong Kong Baptist University.

ISSN (electronic)

19425600

Included in

Mathematics Commons

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