Full friendly index sets and full product-cordial index sets of some permutation petersen graphs
Wai Chee Shiu, Man-Ho Ho · HKBU Institutional Repository (Hong Kong Baptist University) · 2013
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.