New Concepts in Intuitionistic Fuzzy Graph with Application in Water Supplier Systems

In recent years, the concept of domination has been the backbone of research activities in graph theory. The application of graphic domination has become widespread in different areas to solve human-life issues, including social media theories, radio channels, commuter train transportation, earth measurement, internet transportation systems, and pharmacy. The purpose of this paper was to generalize the idea of bondage set (BS) and non-bondage set (NBS), bondage number α(G), and non-bondage number αk(G), respectively, in the intuitionistic fuzzy graph (IFG). The BS is based on a strong arc (SA) in the fuzzy graph (FG). In this research, a new definition of SA in connection with the strength of connectivity in IFGs was applied. Additionally, the BS, α(G), NBS, and αk(G) concepts were presented in IFGs. Three different examples were described to show the informative development procedure by applying the idea to IFGs. Considering the examples, some results were developed. Also, the applications were utilized in water supply systems. The present study was conducted to make daily life more useful and productive.

[1]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[2]  Muhammad Akram,et al.  Certain Concepts in Intuitionistic Neutrosophic Graph Structures , 2017, Inf..

[3]  M. Akram Level graphs of intuitionistic fuzzy graphs , 2018 .

[4]  Muhammad Akram,et al.  q-Rung Orthopair Fuzzy Competition Graphs with Application in the Soil Ecosystem , 2019, Mathematics.

[5]  Ali N. A. Koam,et al.  Granulation of Hypernetwork Models under the q-Rung Picture Fuzzy Environment , 2019, Mathematics.

[6]  Muhammad Akram,et al.  Novel intuitionistic fuzzy soft multiple-attribute decision-making methods , 2016, Neural Computing and Applications.

[7]  Azriel Rosenfeld,et al.  Strong arcs in fuzzy graphs , 2003, Inf. Sci..

[8]  S. Somasundaram,et al.  Domination in fuzzy graphs - I , 1998, Pattern Recognit. Lett..

[9]  Douglas F. Rall,et al.  Bounds on the bondage number of a graph , 1994, Discret. Math..

[10]  Muhammad Akram,et al.  q-Rung Orthopair Fuzzy Hypergraphs with Applications , 2019, Mathematics.

[11]  Michael S. Jacobson,et al.  The bondage number of a graph , 1991, Discret. Math..

[12]  M. G. Karunambigai,et al.  Different types of Domination in Intuitionistic Fuzzy Graph , 2017 .

[13]  Stephen T. Hedetniemi,et al.  Towards a theory of domination in graphs , 1977, Networks.

[14]  Lotfi A. Zadeh,et al.  Similarity relations and fuzzy orderings , 1971, Inf. Sci..

[15]  Muhammad Akram,et al.  Fuzzy Graph Structures with Application , 2019, Mathematics.