Abstract
In this study, the embedding of picture fuzzy graphs on the surface of spheres is introduced. The picture fuzzy genus graph with its genus value and strong (weak) picture fuzzy genus graphs are defined. Some important properties of picture fuzzy genus graphs are discussed. A relation between genus value and degree of planarity of picture fuzzy graph is established. The isomorphism properties of picture fuzzy genus graphs are studied. The Euler polyhedral equation in terms of genus value is established here. Finally, two real-life applications of picture fuzzy genus graph in traffic problem on road network and electronic circuit design on planar sheet are exhibited.
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Das, S., Ghorai, G. & Pal, M. Genus of graphs under picture fuzzy environment with applications. J Ambient Intell Human Comput 12, 10741–10756 (2021). https://doi.org/10.1007/s12652-020-02887-y
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DOI: https://doi.org/10.1007/s12652-020-02887-y