The Non-Adjacency Incompatible Vertices Topology on Digraphs
Keywords:
Directed graphs, Vertices set, Non–adjacency incompatible, Vertices topology, Non–adjacency incompatible , Vertices topological spacesAbstract
In this work, we introduce a new type of topology associated to directed graph on vertices set, which is named as non-adjacency incompatible vertices topology (-topology) of directed graph. A sub-basis family of this topology is generated on the set of vertices, and formed via taking the non-adjacency vertices which arises (path of length two) in different direction to each vertex. We investigate some properties and discuss it on an important and certain types of directed graphs. Our motivation is to giving fundamental steps toward investigation of various properties of directed graphs via their corresponding non-adjacency incompatible vertices topology. Some results are obtained, the presence of the isolated vertex is not necessary in our definition, observations about the specification of this new topology with certain types of digraphs (which type of digraphs achieves the discrete non-adjacency incompatible vertices topology and which does not, and when it achieves and -space). Furthermore, application (applied example in biomathematics) to the Pulmonary circulation in humans is introduced in this paper.
References
Gross, J.L.; Yellen J.; “Handbook of Graph Theory.” 1st ed.; CRC press: Boca Raton, USA, 2003.
Stallings, J.K.; “Topology of finite graphs.” Invent. Math., 71: 551-565, 1983.
Stadler, B.M.; Stadler P.F.; “Generalized topological spaces in evolutionary theory and combinatorial chemistry”. J. Chem. Inf. Comput. Sci., 42 (3): 577-585, 2002.
Ray, S.S.; “Graph Theory with Algorithms and its Applications: In Applied Science and Technology.” 1st ed.; Springer: India, 2013.
Amiri, S.M.; Jafarzadeh, A.; Khatibzadeh, H.; “An Alexandroff topology on graphs.” Bull. Iran. Math. Soc., 39 (4): 647-662, 2013.
Kilicman, A.; Abdulkalek, K.; “Topological spaces associated with simple graphs.” J. Math. Anal., 9 (4): 44-52, 2018.
Hassan, A.F.; Zainy, Z.R.; “The independent compatible edges topology of directed graphs.” J. Discrete Math. Sci. Cryptogr., 25 (8): 2683-2695, 2022.
Ali, I.A.; Hassan, A.F.; “The Independent Incompatible Edges Topology on Di-graphs”. J. Phys.: Conf. Ser., Baghdad, 23-24 March; IOP Publishing Ltd, 2022.
McKinley, M.; O'Loughlin, V.D.; “Human Anatomy.” 3rd ed.; McGraw-Hill, 2011.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Zahraa L. Hadi, Asmhan F. Hassan
This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg)
