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Product Operations on q-Rung Orthopair Fuzzy Graphs

School of Management Engineering and Business, Hebei University of Engineering, Handan 056038, China
Author to whom correspondence should be addressed.
Symmetry 2019, 11(4), 588;
Received: 11 March 2019 / Revised: 16 April 2019 / Accepted: 18 April 2019 / Published: 23 April 2019
PDF [950 KB, uploaded 23 April 2019]


The q-rung orthopair fuzzy graph is an extension of intuitionistic fuzzy graph and Pythagorean fuzzy graph. In this paper, the degree and total degree of a vertex in q-rung orthopair fuzzy graphs are firstly defined. Then, some product operations on q-rung orthopair fuzzy graphs, including direct product, Cartesian product, semi-strong product, strong product, and lexicographic product, are defined. Furthermore, some theorems about the degree and total degree under these product operations are put forward and elaborated with several examples. In particular, these theorems improve the similar results in single-valued neutrosophic graphs and Pythagorean fuzzy graphs. View Full-Text
Keywords: q-rung orthopair fuzzy graph; product operations; q-rung orthopair fuzzy sets; total degree q-rung orthopair fuzzy graph; product operations; q-rung orthopair fuzzy sets; total degree

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Yin, S.; Li, H.; Yang, Y. Product Operations on q-Rung Orthopair Fuzzy Graphs. Symmetry 2019, 11, 588.

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