In this article, a technique to construct a new type of topological structures by graphs called topological graphs is introduced. We use the concept of a homeomorphism between topological graphs as a topological property to prove the isomorphic between graphs. We construct a computer program that builds graphs and its topological graphs. This model helps in studying many topological properties such as continuity, connectedness, compactness and separation axioms on graphs. Finally, we present some examples of different types of graphs and their topological graphs and study some of their topological and algebraic properties.
AkramM., m-Polar Fuzzy Graphs, Studies in Fuzziness and Soft Computing, Springer, 2019.
2.
Bondy A.J., Murty R.S.U., Graph theory with applications, Elsevier Science Publishing Company Inc, 1975.
3.
Cain L.G., Introduction to general, Addison Wesley Publishing Company, Inc, 1994.
4.
DiestelR., Graph theory II, Heidelberg, Springer-Verlag IV, 2010.
5.
El-NaschieS.M., Topics in the mathematical physics of Einfinity theory, Chaos, Solitons, Fractals30 (2006), 656–663.
6.
El-SharkasyM.M., BadrS.M., Topological spaces via phenotype- genotype spaces, International Journal of Biomathematics9(4) (2016), 1–16.
7.
El-SharkasyM.M., BadrS.M., Modeling DNA and RNA mutation using mset and topology, International Journal of Biomathematics11(04) (2018).
8.
El-SharkasyM.M., ShokryM., Separation axioms under crossover operator and its generalized, International Journal of Biomathematics9(4) (2016), 1–23.
9.
JiangH., ZhanJ., ChenD., Covering based variable precision (I, T)-fuzzy rough sets with applications to multi-attribute decision-making, IEEE Transactions on Fuzzy Systems (2018) doi:10.1109/TFUZZ.2018.2883023.
10.
Chartrand G., Lesniak L., Zhang P., Textbooks in Mathematics(Graphs and Digraphs), Sixth Edition, 2016.
11.
GaltonA., A generalized topological view of motion in discrete space, Theoretical Computer Science305 (2003), 111–134.
12.
NadaS.I., El-AtikA.A., AtefM., New types of topological structures via graphs, Mathematical Methods in the Applied Sciences41 (2018), 5801–5810.
13.
NawarA.S., El AtikA.A., A model of a human heart via graph nano topological spaces, International Journal of Biomathematics12(1) (2019).
StadlerB.M.R., StadlerP.F., Generalized topological spaces in evolutionary theory and combinatorial chemistry, Journal of Chemical Information and Computer Sciences42 (2002), 577–585.
16.
Morris S.A., Topology without tears, version of March 1, 2017.
17.
ShokryM., AlyR.E., Topological properties on graph VS medical application in human heart, International Journal of Applied Mathematics15 (2013), 1103–1109.
18.
Wilson R.J., Rough sets, Introduction to graph theory, Fourth Edition, Longmon Maleysia, 1996.
19.
ZhanJ., SunB., AlcantudJ.C.R., Covering based multigranulation (I, T)-fuzzy rough set models and applications in multi-attribute group decision-making, Information Sciences476 (2019), 290–318.
20.
ZhangK., ZhanJ., WuW., AlcantudJ.C.R., Fuzzy β-covering based (I; T)-fuzzy rough set models and applications to multi-attribute decision-making, Computers & Industrial Engineering128 (2019), 605–621.
21.
ZhangL., ZhanJ., XuZ., Covering-based generalized IF rough sets with applications to multi-attribute decision-making, Information Sciences478 (2019), 275–302.
