Department of Mathematics
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.
Full friendly indexsets, full product-cordial index sets, permutationPetersen graph
Source Publication Title
Journal of Combinatorics and Number Theory
Nova Science Publishers
© NovaSciencePublishers, Inc.
This work is partially supported by the Faculty Research Grant, Hong Kong Baptist University.
Link to Publisher's Edition
Shiu, Wai Chee, and Man-Ho Ho. "Full friendly index sets and full product-cordial index sets of some permutation petersen graphs." Journal of Combinatorics and Number Theory 5.3 (2013): 227-244.