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Libration points in the restricted three-body problem: Euler angles, existence and stability
Tight independent set neighborhood union condition for fractional critical deleted graphs and ID deleted graphs
1. | Faculty of Information Studies, Novo Mesto, Slovenia |
2. | Institut für Informatik, Freie Universität Berlin, Takustraße, D-4195 Berlin, Germany |
$ (g,f,n',m) $ |
$ δ(G)≥\frac{b^{2}(i-1)}{a}+n'+2m $ |
$ n>\frac{(a+b)(i(a+b)+2m-2)+bn'}{a} $ |
$|N_{G}(x_{1})\cup N_{G}(x_{2})\cup···\cup N_{G}(x_{i})|≥\frac{b(n+n')}{a+b}$ |
$ \{x_{1},x_{2},..., x_{i}\} $ |
$ V(G) $ |
$ (g,f,m) $ |
References:
[1] |
E. I. Abouelmagd and J. L. G. Guirao, On the perturbed restricted three-body problem, Appl. Math. Nonl. Sc., 1 (2016), 123-144. Google Scholar |
[2] |
J. A. Bondy and U. S. R. Mutry, Graph Theory, Springer, Berlin, 2008.
doi: 10.1007/978-1-84628-970-5. |
[3] |
R. Y. Chang, G. Z. Liu and Y. Zhu,
Degree conditions of fractional ID-$k$-factor-critical graphs, Bull. Malays. Math. Sci. Soc., 33 (2010), 355-360.
|
[4] |
W. Gao, Some Results on Fractional Deleted Graphs, Doctoral disdertation of Soochow university, 2012. Google Scholar |
[5] |
W. Gao, L. Liang, T. W. Xu and J. X. Zhou,
Degree conditions for fractional $ (g,f,n',m) $-critical deleted graphs and fractional ID-$ (g,f,m) $-deleted graphs, Bull. Malays. Math. Sci. Soc., 39 (2016), 315-330.
doi: 10.1007/s40840-015-0194-1. |
[6] |
W. Gao, Y. Guo and K. Y. Wang, Ontology algorithm using singular value decomposition and applied in multidisciplinary, Cluster Comput., 19 (2016), 2201-2210. Google Scholar |
[7] |
W. Gao, L. Liang, T. W. Xu and J. X. Zhou,
Tight toughness condition for fractional $(g, f, n)$-critical graphs, J. Korean Math. Soc., 51 (2014), 55-65.
doi: 10.4134/JKMS.2014.51.1.055. |
[8] |
W. Gao and W. F. Wang,
The fifth geometric arithmetic index of bridge graph and carbon nanocones, J. Differ. Equ. Appl., 23 (2017), 100-109.
doi: 10.1080/10236198.2016.1197214. |
[9] |
W. Gao and W. F. Wang,
The eccentric connectivity polynomial of two classes of nanotubes, Chaos Soliton. Fract., 89 (2016), 290-294.
doi: 10.1016/j.chaos.2015.11.035. |
[10] |
W. Gao, J. L. G. Guirao and H. L. Wu,
Two tight independent set conditions for fractional $(g, f, m)$-deleted graphs systems, Qual. Theory Dyn. Syst., 17 (2018), 231-243.
doi: 10.1007/s12346-016-0222-z. |
[11] |
J. L. G. Guirao and A. C. J. Luo,
New trends in nonlinear dynamics and chaoticity, Nonlinear Dynam., 84 (2016), 1-2.
doi: 10.1007/s11071-016-2656-x. |
[12] |
S. Z. Zhou, Z. R. Sun and Z. R. Xu,
A result on $r$-orthogonal factorizations in digraphs, Eur. J. Combin., 65 (2017), 15-23.
doi: 10.1016/j.ejc.2017.05.001. |
[13] |
S. Z. Zhou, F. Yang and Z. R. Sun,
A neighborhood condition for fractional ID-$[a, b]$-factor-critical graphs, Discuss. Mathe. Graph T., 36 (2016), 409-418.
doi: 10.7151/dmgt.1864. |
[14] |
S. Z. Zhou, L. Xu and Y. Xu, A sufficient condition for the existence of a $k$-factor excluding a given $r$-factor, Appl. Math. Nonl. Sc., 2 (2017), 13-20. Google Scholar |
[15] |
S. Z. Zhou, Some Results about Component Factors in Graphs, RAIRO-Oper. Res., 2017.
doi: 10.1051/ro/2017045. |
[16] |
S. Z. Zhou, Z. R. Sun and H. Liu,
A minimum degree condition for fractional ID-[$ a,b $]-factor-critical graphs, Bull. Aust. Math. Soc., 86 (2012), 177-183.
doi: 10.1017/S0004972711003467. |
show all references
References:
[1] |
E. I. Abouelmagd and J. L. G. Guirao, On the perturbed restricted three-body problem, Appl. Math. Nonl. Sc., 1 (2016), 123-144. Google Scholar |
[2] |
J. A. Bondy and U. S. R. Mutry, Graph Theory, Springer, Berlin, 2008.
doi: 10.1007/978-1-84628-970-5. |
[3] |
R. Y. Chang, G. Z. Liu and Y. Zhu,
Degree conditions of fractional ID-$k$-factor-critical graphs, Bull. Malays. Math. Sci. Soc., 33 (2010), 355-360.
|
[4] |
W. Gao, Some Results on Fractional Deleted Graphs, Doctoral disdertation of Soochow university, 2012. Google Scholar |
[5] |
W. Gao, L. Liang, T. W. Xu and J. X. Zhou,
Degree conditions for fractional $ (g,f,n',m) $-critical deleted graphs and fractional ID-$ (g,f,m) $-deleted graphs, Bull. Malays. Math. Sci. Soc., 39 (2016), 315-330.
doi: 10.1007/s40840-015-0194-1. |
[6] |
W. Gao, Y. Guo and K. Y. Wang, Ontology algorithm using singular value decomposition and applied in multidisciplinary, Cluster Comput., 19 (2016), 2201-2210. Google Scholar |
[7] |
W. Gao, L. Liang, T. W. Xu and J. X. Zhou,
Tight toughness condition for fractional $(g, f, n)$-critical graphs, J. Korean Math. Soc., 51 (2014), 55-65.
doi: 10.4134/JKMS.2014.51.1.055. |
[8] |
W. Gao and W. F. Wang,
The fifth geometric arithmetic index of bridge graph and carbon nanocones, J. Differ. Equ. Appl., 23 (2017), 100-109.
doi: 10.1080/10236198.2016.1197214. |
[9] |
W. Gao and W. F. Wang,
The eccentric connectivity polynomial of two classes of nanotubes, Chaos Soliton. Fract., 89 (2016), 290-294.
doi: 10.1016/j.chaos.2015.11.035. |
[10] |
W. Gao, J. L. G. Guirao and H. L. Wu,
Two tight independent set conditions for fractional $(g, f, m)$-deleted graphs systems, Qual. Theory Dyn. Syst., 17 (2018), 231-243.
doi: 10.1007/s12346-016-0222-z. |
[11] |
J. L. G. Guirao and A. C. J. Luo,
New trends in nonlinear dynamics and chaoticity, Nonlinear Dynam., 84 (2016), 1-2.
doi: 10.1007/s11071-016-2656-x. |
[12] |
S. Z. Zhou, Z. R. Sun and Z. R. Xu,
A result on $r$-orthogonal factorizations in digraphs, Eur. J. Combin., 65 (2017), 15-23.
doi: 10.1016/j.ejc.2017.05.001. |
[13] |
S. Z. Zhou, F. Yang and Z. R. Sun,
A neighborhood condition for fractional ID-$[a, b]$-factor-critical graphs, Discuss. Mathe. Graph T., 36 (2016), 409-418.
doi: 10.7151/dmgt.1864. |
[14] |
S. Z. Zhou, L. Xu and Y. Xu, A sufficient condition for the existence of a $k$-factor excluding a given $r$-factor, Appl. Math. Nonl. Sc., 2 (2017), 13-20. Google Scholar |
[15] |
S. Z. Zhou, Some Results about Component Factors in Graphs, RAIRO-Oper. Res., 2017.
doi: 10.1051/ro/2017045. |
[16] |
S. Z. Zhou, Z. R. Sun and H. Liu,
A minimum degree condition for fractional ID-[$ a,b $]-factor-critical graphs, Bull. Aust. Math. Soc., 86 (2012), 177-183.
doi: 10.1017/S0004972711003467. |
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