Fuzzy topological spaces on fuzzy graphs
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper we study interrelation between fuzzy graphs and fuzzy topological spaces. We have introduced various fuzzy topological spaces on simple connected fuzzy graphs by using adjacency relation. Some characterization theorems for fuzzy topologies related to isomorphic fuzzy graphs, weak isomorphic fuzzy graphs and co-week isomorphic fuzzy graphs are given. Interior, closure properties, $T_{1}$ and $T_{2}$ separation axioms for these fuzzy topological spaces are studied. In last section we define neighborhood fuzzy topological spaces on simple fuzzy graph and establish a linkage between fuzzy topology and fuzzy graph.
Abstract
In this paper we study interrelation between fuzzy graphs and fuzzy topological spaces. We have introduced various fuzzy topological spaces on simple connected fuzzy graphs by using adjacency relation. Some characterization theorems for fuzzy topologies related to isomorphic fuzzy graphs, weak isomorphic fuzzy graphs and co-week isomorphic fuzzy graphs are given. Interior, closure properties, $T_{1}$ and $T_{2}$ separation axioms for these fuzzy topological spaces are studied. In last section we define neighborhood fuzzy topological spaces on simple fuzzy graph and establish a linkage between fuzzy topology and fuzzy graph.
참고문헌 (18)
- S. Amiri, "An Alexandroff topology on graphs", Bulletin of the Iranian Mathematical Society, 39, pp.647~662 (2013)
- A. Kilicman, "Topological spaces associated with simple graphs", Journal of Mathematical Analysis, 9, pp.44~52 (2018)
- H. Sari, "On topological spaces generated by simple undirected graphs", AIMS Mathematics, 5, pp.5541~5550 (2020)
- T. Ibraheem, "On topological spaces generated by graphs and vice versa", Journal of Al-Quadisiyah for Computer Science and Mathematics, 13, pp.13~24 (2021)
- P. S. Gholap, "Topological spaces generated by graph", Jnanabha, 52, pp.1~7 (2022)
- C. L. Chang, "Fuzzy topological spaces", J. Math. Anal. Appl, 24, pp.182~190 (1968)
- A. Rosenfield, "Fuzzy Graphs", pp.77~95 (1975), Academic Press
- T. Pramanik, "An Extension of fuzzy competition graph and its uses in manufacturing industries", Mathematics, 8, pp.1~23 (2020)
- H. Rashmanlou, "A Study on cubic graphs with novel application", Journal of Intelligent and Fuzzy Systems, 40(1), pp.89~101 (2021)
- G. Muhiuddin, "Reinforcement number of a graph with respect to half-domination", Journal of Mathematics, 3, pp.1~7 (2021)
- S. Amanathulla, "Distance two surjective labelling of paths and interval graphs", Discrete Dynamics in Nature and Society, 14, pp.1~9 (2021)
- M. Atef, "Fuzzy topological structures via fuzzy graphs and their applications", Soft Computing, 25, pp.6013~6027
- L. A. Zadeh, "Fuzzy Sets", Information and Control, 8, pp.338~353 (1965)
- J. N. Mordeson, "Fuzzy Graphs and Fuzzy Hypergraphs" (2000), Physica Verlag
- A. Somasundaram, "Domination in fuzzy graphs", Pattern Recognition Letters, 19, pp.787~791 (1998)
- Pu Pao-Ming, "Fuzzy topology I. Neighborhood structure of a fuzzy point and Moore-Smith convergence", J. Math. Anal. Appl, 76, pp.571~599 (1980)
- R. Srivastava, "Topics in Fuzzy Topology", Ph.D, pp.1984
- M. S. Sunitha, "Complement of fuzzy graph", Indian Journal of Pure and Applied Mathematics, 33(9), pp.1451~1464 (2002)