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A NEIGHBOURHOOD CONDITION FOR GRAPHS TO BE FRACTIONAL (k, m)-DELETED GRAPHS*

Published online by Cambridge University Press:  30 July 2009

SIZHONG ZHOU
SIZHONG ZHOU*
Affiliation:
School of Mathematics and Physics, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang, Jiangsu 212003, People's Republic of China e-mail: [email protected]
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Abstract

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Let G be a connected graph of order n, and let k ≥ 2 and m ≥ 0 be two integers. In this paper, we show that G is a fractional (k, m)-deleted graph if and for each pair of non-adjacent vertices x, y of G. This result is an extension of the previous result of Zhou [11].

Keywords

05C70
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 1 , January 2010 , pp. 33 - 40
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Bondy, J. A. and Murty, U. S. R., Graph theory with applications (The Macmillan Press, London, 1976).CrossRefGoogle Scholar
2.Correa, J. R. and Matamala, M., Some remarks about factors of graphs, J. Graph Theory 57 (2008), 265–274.CrossRefGoogle Scholar
3.Iida, T. and Nishimura, T., Neighborhood conditions and k-factors, Tokyo J. Math. 20 (2) (1997), 411–418.CrossRefGoogle Scholar
4.Liu, G. and Zhang, L., Fractional (g, f)-factors of graphs, Acta Math. Sci. 21B (4) (2001), 541–545.CrossRefGoogle Scholar
5.Liu, G. and Zhang, L., Toughness and the existence of fractional k-factors of graphs, Discrete Math. 308 (2008), 1741–1748.CrossRefGoogle Scholar
6.Scheinerman, E. R. and Ullman, D. H., Fractional graph theory (Wiley, New York, 1997).Google Scholar
7.Yu, J., Liu, G., Ma, M. and Cao, B., A degree condition for graphs to have fractional factors, Adv. Math. (China) 35 (5) (2006), 621–628.Google Scholar
8.Zhou, S., Some sufficient conditions for graphs to have (g, f)-factors, Bull. Aust. Math. Soc. 75 (2007), 447–452.CrossRefGoogle Scholar
9.Zhou, S., A new sufficient condition for graphs to be (g, f, n)-critical graphs, Can. Math. Bull. (to appear).Google Scholar
10.Zhou, S., Remarks on (a, b, k)-critical graphs, J. Comb. Math. Comb. Comput. (to appear).Google Scholar
11.Zhou, S. and Liu, H., Neighborhood conditions and fractional k-factors, Bull. Malaysian Math. Sci. Soc. 32 (1) (2009), 37–45.Google Scholar