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Full friendly index sets of slender and flat cylinder graphs | ||
| Transactions on Combinatorics | ||
| مقاله 6، دوره 2، شماره 4، اسفند 2013، صفحه 63-80 اصل مقاله (367.75 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2013.3678 | ||
| نویسندگان | ||
| Wai Chee Shiu* ؛ Man-Ho Ho | ||
| Hong Kong Baptist University | ||
| چکیده | ||
| Let $G=(V,E)$ be a connected simple graph. A labeling $f:V \to Z_2$ induces an edge labeling $f^*:E \to Z_2$ defined by $f^*(xy)=f(x)+f(y)$ for each $xy \in E$. For $i \in Z_2$, let $v_f(i)=|f^{-1}(i)|$ and $e_f(i)=|f^{*-1}(i)|$. A labeling $f$ is called friendly if $|v_f(1)-v_f(0)|\le 1$. The full friendly index set of $G$ consists all possible differences between the number of edges labeled by 1 and the number of edges labeled by 0. In recent years, full friendly index sets for certain graphs were studied, such as tori, grids $P_2\times P_n$, and cylinders $C_m\times P_n$ for some $n$ and $m$. In this paper we study the full friendly index sets of cylinder graphs $C_m\times P_2$ for $m\geq 3$, $C_m\times P_3$ for $m\geq 4$ and $C_3\times P_n$ for $n\geq 4$. The results in this paper complement the existing results in literature, so the full friendly index set of cylinder graphs are completely determined. | ||
| کلیدواژه‌ها | ||
| Full friendly index sets؛ friendly labeling؛ cylinder graphs | ||
| مراجع | ||
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W. C. Shiu and H. Kwong (2008) Full friendly index sets of {P}_2\times{P}_n Discrete Math. 308, 3688-3693
W. C. Shiu and M. H. Ling (2007) Extreme friendly indices of {$C_m\times C_n$} Congr. Numer. 188, 175-182
W. C. Shiu and M. H. Ling (2010) Full friendly index sets of {C}artesian products
of two cycles Acta Math. Sin. (Engl. Ser.) 26, 1233-1244
W. C. Shiu and F. S. Wong (2009) W. C. Shiu and F. S. Wong Congr. Numer. 197, 65-75
W. C. Shiu and F. S. Wong (2012) Full friendly index sets of cylinder graphs Australas. J. Combin. 52, 141-162
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