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q-rung picture fuzzy graphs: a creative view on regularity with applications

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Abstract

The q-rung picture fuzzy set model, superior to picture and spherical fuzzy set models, broaden the space of uncertain and vague information due to its outstanding feature of vast depiction space of admissible triplets. In this paper, we introduce the notion of q-rung picture fuzzy graphs and discuss regularity of these graphs. We present geometrical interpretation under q-rung picture fuzzy environment. We illustrate strongly regular, perfectly regular and regular uniform q-rung picture fuzzy graphs. Motivated by some real world situations, we propose the novel concept of m-partite q-rung picture fuzzy graphs with several insightful results on their regularity, named as m-regularity. Moreover, we introduce q-rung picture fuzzy line graphs and develop a necessary condition for regular q-RPFLGs. In addition, we present an application to investigate this broad representation space in graph-theoretical concepts.

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  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, 4590, Pakistan

    Muhammad Akram & Amna Habib

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  1. Muhammad Akram
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Akram, M., Habib, A. q-rung picture fuzzy graphs: a creative view on regularity with applications. J. Appl. Math. Comput. 61, 235–280 (2019). https://doi.org/10.1007/s12190-019-01249-y

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