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Product-cordial index and friendly index of regular graphs | ||
| Transactions on Combinatorics | ||
| مقاله 3، دوره 1، شماره 1، خرداد 2012، صفحه 15-20 اصل مقاله (431.85 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2012.482 | ||
| نویسندگان | ||
| Wai Chee Shiu* 1؛ Kwong Harris2 | ||
| 1Hong Kong Baptist University | ||
| 2State University of New York at Fredonia | ||
| چکیده | ||
| 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 $\{i^+_f(G)\;|\;f \mbox{ is a friendly labeling of} G\}$ 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 $\{i^*_f(G)\;|\;f \mbox{ is a friendly labeling of} G\}$ 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. | ||
| کلیدواژهها | ||
| friendly labeling؛ friendly index set؛ product-cordial index؛ product-cordial index set؛ Torus | ||
| مراجع | ||
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