ISSN Print: 2381-1234  ISSN Online: 2381-1242
AASCIT Journal of Nanoscience  
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Some Properties on Nano Topology Induced by Graphs
AASCIT Journal of Nanoscience
Vol.3 , No. 4, Publication Date: Sep. 8, 2017, Page: 19-23
493 Views Since September 8, 2017, 1619 Downloads Since Sep. 8, 2017
 
 
Authors
 
[1]    

Arafa Nasef, Department of Physics and Engineering Mathematics, Faculty of Engineering, Kafrelsheikh University, Kafrelsheikh, Egypt.

[2]    

Abd El Fattah El-Atik, Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.

 
Abstract
 

A nano topological space became a new type of modern topology in terms of rough sets. The paper aims to analyze some real life problems using nano topology. We point out that some examples and results as proposed by Lellis Thivagar et al. (2016) are not true. The corrections will improve further extensions of the results in [1]. Some new forms of topological structures on a simple directed graph and give more generalized nano topology induced by graphs will be established.


Keywords
 

Graphs, Rough Sets, Relation, Nano Topological Graphs


Reference
 
[01]    

Lellis Thivagar, M.; Paul Manuel and Sutha Devi, V.: A detection for patent infringement suit via nanotopology induced by graph, Cogent Mathematics, 3, (2016), 1-10.

[02]    

Wilson, R. J.: Introduction to graph theory, Fourth Edition, Longmon Maleysia (1996).

[03]    

Bondy, J. A. and Murty, U. S. R.: Graph theory with applications, Elsevier Science Publishing Co. Inc. (1975).

[04]    

Diestel, R.: Graph theory II, Heidelberg, Springer-Verlag IV, (2010).

[05]    

Boninowski, Z.; Bryniarski, E. and Wybraniec, U.: Extensions and intensions in the rough set theory, Information Sciences, 107, (1998), 149-167.

[06]    

Lellis Thivagar, M. and Richard, C.: On nano forms of weakly open sets, International Journal of Mathematics and Statistics, 1, (2013), 31-37.

[07]    

Lellis Thivagar, M. and Richard, C.: On nano continuity, Journal of Mathematical Theory and Modelling, 3, (2013), 32-37.

[08]    

Pawlak, Z.: Rough sets, Theoretical Aspects of Reasoning About Data, Kluwer Acadmic Publishers Dordrecht, 1991.

[09]    

Bondy, J. A. and Murty, U. S. R.: Graph theory with applications, Elsevier Science Publishing Co. Inc. (1975).

[10]    

M. S. El Naschie, Topics in the mathematical physics of E-infinity theory, Chaos, Solitons, Fractals 30 (2006), 656-663.





 
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