%0 Journal Article
%T Product-cordial index and friendly index of regular graphs
%A Wai Chee Shiu
%A Kwong Harris
%J Transactions on Combinatorics
%D 2012
%I University of Isfahan
%X Let $G=(V,E)$ be a connected simple graph. A labeling $f:V to Z_2$ induces two edge labelings $f^+, f^*: E to Z_2$ defined by $f^+(xy) = f(x)+f(y)$ and $f^*(xy) = f(x)f(y)$ for each $xy in E$. For $i in Z_2$, let $v_f(i) = |f^{-1}(i)|$, $e_{f^+}(i) = |(f^{+})^{-1}(i)|$ and $e_{f^*}(i) = |(f^*)^{-1}(i)|$. A labeling $f$ is called friendly if $|v_f(1)-v_f(0)| le 1$. For a friendly labeling $f$ of a graph $G$, the friendly index of $G$ under $f$ is defined 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 $G$. Also, the product-cordial index of $G$ under $f$ is defined 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 product-cordial index set of $G$. In this paper, we find a relation between the friendly index and the product-cordial index of a regular graph. As applications, we will determine the full product-cordial index sets of torus graphs which was asked by Kwong, Lee and Ng in 2010; and those of cycles.
%K Friendly labeling
%K friendly index set
%K product-cordial index
%K product-cordial index set
%K torus
%U http://www.combinatorics.ir/?_action=showPDF&article=482&_ob=0f0636556a2c2f345a1e9f8e54e0934d&fileName=full_text.pdf