پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 44 |
| تعداد شمارهها | 1,877 |
| تعداد مقالات | 15,278 |
| تعداد مشاهده مقاله | 43,730,765 |
| تعداد دریافت فایل اصل مقاله | 17,563,107 |
Extreme edge-friendly indices of complete bipartite graphs | ||
| Transactions on Combinatorics | ||
| مقاله 54، دوره 5، شماره 3، آذر 2016، صفحه 11-21 اصل مقاله (240.45 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2016.12473 | ||
| نویسنده | ||
| Wai Chee Shiu* | ||
| Hong Kong Baptist University | ||
| چکیده | ||
| Let $G=(V,E)$ be a simple graph. An edge labeling $f:E\to \{0,1\}$ induces a vertex labeling $f^+:V\to Z_2$ defined by $f^+(v)\equiv \sum\limits_{uv\in E} f(uv)\pmod{2}$ for each $v \in V$, where $Z_2=\{0,1\}$ is the additive group of order 2. For $i\in\{0,1\}$, let $e_f(i)=|f^{-1}(i)|$ and $v_f(i)=|(f^+)^{-1}(i)|$. A labeling $f$ is called edge-friendly if $|e_f(1)-e_f(0)|\le 1$. $I_f(G)=v_f(1)-v_f(0)$ is called the edge-friendly index of $G$ under an edge-friendly labeling $f$. Extreme values of edge-friendly index of complete bipartite graphs will be determined. | ||
| کلیدواژهها | ||
| edge-friendly index؛ edge-friendly labeling؛ complete bipartite graph | ||
| مراجع | ||
|
[1] K. L. Collins and M. Hovey, Most graphs are edge cordial, Ars Combin., 30 (1990) 289–295. [2] H. Kwong, S. M. Lee and H. K. Ng, On friendly index sets of 2-regular graphs, Discrete Math., 308 (2008) 5522–5532. [3] H. Kwong and S. M. Lee, On friendly index sets of generalized books, J. Combin. Math. Combin. Comput., 66 (2008) 43–58. [4] S. M. Lee and H. K. Ng, A conjecture on edge cordial trees, Amer. Math. Soc., 9 (1988) 286–287. [5] S. M. Lee and H. K. Ng, On friendly index sets of bipartite graphs, Ars Combin., 86 (2008) 257–271. [6] E. Salehi and S. M. Lee, On friendly index sets of trees, Congr. Numer., 178 (2006) 173–183. [7] W. C. Shiu and M. H. Ho, Full friendly index sets and full product-cordial index sets of some permutation Petersen graphs, J. Comb. Number Theory, 5 (2013) 227–244. [8] W. C. Shiu and M. H. Ho, Full friendly index sets of slender and flat cylinder graphs, Trans. Comb., 2 no. 4 (2013) 63–80. [9] W. C. Shiu and H. Kwong, Full friendly index sets of ${P}_2times{P}_n$, Discrete Math., 308 (2008) 3688–3693. [10] W. C. Shiu and H. Kwong, Product-cordial index and friendly index of regular graphs, Trans. Comb., 1 no. 1 (2012) 15–20. [11] W. C. Shiu and S. M. Lee, Full friendly index sets and full product-cordial index sets of twisted cylinders, J. Comb. Number Theory, 3 (2012) 209–216. [12] W. C. Shiu and M. H. Ling, Full friendly index sets of Cartesian products of two cycles, Acta Math. Sin. (Engl. Ser.), 26 (2010) 1233–1244. [13] W. C. Shiu and F. S. Wong, Full friendly index sets of cylinder graphs, Australas. J. Combin., 52 (2012) 141–162. [14] D. Sinha and J. Kaur, Full friendly index set-I, Discrete Appl. Math., 161 (2013) 1262–1274. [15] D. Sinha and J. Kaur, Full friendly index set-II, J. Combin. Math. Combin. Comput., 79 (2011) 65–75. [16] D. West, Introduction to Graph Theory,Prentice Hall, Inc., Upper Saddle River, NJ, 1996. | ||
|
آمار تعداد مشاهده مقاله: 3,320 تعداد دریافت فایل اصل مقاله: 2,819 |
||