Korean J. Math. Vol. 31 No. 4 (2023) pp.485-494
DOI: https://doi.org/10.11568/kjm.2023.31.4.485

On beta product of hesitancy fuzzy graphs and intuitionistic hesitancy fuzzy graphs

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Published: Dec 30, 2023
Keywords:
Hesitancy fuzzy graph,, Intuitionistic hesitancy fuzzy graph, Strong intuitionistic hesitancy fuzzy graph, Complete intuitionistic hesitancy fuzzy graph, $\beta$-product
Mathematics Subject Classification:
05C72, 05C76

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Sunil. M.P
PG and Research Department of Mathematics, N.S.S. Hindu College, Changanacherry, Kottayam, Kerala 686102, India
J. Suresh Kumar
PG and Research Department of Mathematics, N.S.S. Hindu College, Changanacherry, Kottayam, Kerala 686102, India

Abstract

The degree of hesitancy of a vertex in a hesitancy fuzzy graph depends on the degree of membership and non-membership of the vertex. We define a new class of hesitancy fuzzy graph, the intuitionistic hesitancy fuzzy graph in which the degree of hesitancy of a vertex is independent of the degree of its membership and non-membership. We introduce the idea of $\beta$-product of a pair of hesitancy fuzzy graphs and intuitionistic hesitancy fuzzy graphs and prove certain results based on this product.



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