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Gao, Yun, Farahani, Mohammad Reza, Gao, Wei. (1395). A neighborhood union condition for fractional $(k,n',m)$-critical deleted graphs. , 6(1), 13-19. doi: 10.22108/toc.2017.20355
Yun Gao; Mohammad Reza Farahani; Wei Gao. "A neighborhood union condition for fractional $(k,n',m)$-critical deleted graphs". , 6, 1, 1395, 13-19. doi: 10.22108/toc.2017.20355
Gao, Yun, Farahani, Mohammad Reza, Gao, Wei. (1395). 'A neighborhood union condition for fractional $(k,n',m)$-critical deleted graphs', , 6(1), pp. 13-19. doi: 10.22108/toc.2017.20355
Gao, Yun, Farahani, Mohammad Reza, Gao, Wei. A neighborhood union condition for fractional $(k,n',m)$-critical deleted graphs. , 1395; 6(1): 13-19. doi: 10.22108/toc.2017.20355

A neighborhood union condition for fractional $(k,n',m)$-critical deleted graphs

Transactions on Combinatorics
مقاله 2، دوره 6، شماره 1، خرداد 2017، صفحه 13-19    اصل مقاله (225.47 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2017.20355
نویسندگان
Yun Gao1؛ Mohammad Reza Farahani2؛ Wei Gao* 3
1Department of Editorial, Yunnan Normal University
2Department of Applied Mathematics, Iran University of Science and Technology
3School of Information and Technology, Yunnan Normal University
چکیده
A graph $G$ is called a fractional‎ ‎$(k,n',m)$-critical deleted graph if any $n'$ vertices are removed‎ ‎from $G$ the resulting graph is a fractional $(k,m)$-deleted‎ ‎graph‎. ‎In this paper‎, ‎we prove that for integers $k\ge 2$‎, ‎$n',m\ge0$‎, ‎$n\ge8k+n'+4m-7$‎, ‎and $\delta(G)\ge k+n'+m$‎, ‎if‎ ‎$$|N_{G}(x)\cup N_{G}(y)|\ge\frac{n+n'}{2}$$‎ ‎for each pair of non-adjacent vertices $x$‎, ‎$y$ of $G$‎, ‎then $G$‎ ‎is a fractional $(k,n',m)$-critical deleted graph‎. ‎The bounds for‎ ‎neighborhood union condition‎, ‎the order $n$ and the minimum degree‎ ‎$\delta(G)$ of $G$ are all sharp‎.
کلیدواژه‌ها
‎Graph‎؛ ‎fractional‎ ‎factor‎؛ ‎fractional $(k؛ n'؛ m)$-critical deleted graph‎؛ ‎neighborhood‎ ‎union condition
مراجع
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[10] S. Z. Zhou, A sufficient condition for a graph to b e a fractional ( f ; n )-critical graph, Glasg. Math. J. , 52 (2010) 409-415.

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