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Maximal strong product and balanced fuzzy graphs
Talal Al-Hawary 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.5
The notion of maximal product of two fuzzy graphs was introduced by Radha and Arumugam in 2015 and the notion of balanced fuzzy graph was introduced by Al-Hawary in 2011. In this paper, we give a modification of the maximal product definition, which we call maximal strong product. We also introduce the relatively new notion of maximal-balanced fuzzy graphs. We give necessary and sufficient conditions for the maximal strong product of two balanced (resp., maximal-balanced) fuzzy graphs to be balanced (resp., maximal-balanced) and we prove that these two independent notions are preserved under isomorphism.
Talal Al-Hawary 대한수학회 2008 대한수학회보 Vol.45 No.4
In this paper, we introduce the relatively new notion of fuzzy ωO-open set. We prove that the collection of all fuzzy ωO-open subsets of a fuzzy topological space forms a fuzzy topology that is finer than the original one. Several characterizations and properties of this class are also given as well as connections to other well-known “fuzzy generalized open” subsets. In this paper, we introduce the relatively new notion of fuzzy ωO-open set. We prove that the collection of all fuzzy ωO-open subsets of a fuzzy topological space forms a fuzzy topology that is finer than the original one. Several characterizations and properties of this class are also given as well as connections to other well-known “fuzzy generalized open” subsets.
COMPLETE HAMACHER FUZZY GRAPHS
AL-HAWARY, TALAL ALI The Korean Society for Computational and Applied M 2022 Journal of applied mathematics & informatics Vol.40 No.5-6
Our goal in this paper is to propose the advancement proposed by Alsina, Klement and other researchers in the area of fuzzy logic applied to the area of fuzzy graph theory. We introduce the notion of complete Hamacher fuzzy graphs and the notion of balanced Hamacher fuzzy graphs and discuss their properties. Moreover, several operations on these fuzzy graphs are explored via the complete notion.
Al-Hawary, Talal Korean Mathematical Society 2008 대한수학회보 Vol.45 No.4
In this paper, we introduce the relatively new notion of fuzzy ${\omega}^O$-open set. We prove that the collection of all fuzzy ${\omega}^O$-open subsets of a fuzzy topological space forms a fuzzy topology that is finer than the original one. Several characterizations and properties of this class are also given as well as connections to other well-known "fuzzy generalized open" subsets.
beta-product of product fuzzy graphs
Talal Ali Al-Hawary,Maref Y.M. Alzoubi 한국전산응용수학회 2024 Journal of applied mathematics & informatics Vol.42 No.2
In this article, a new operation on product fuzzy graphs (PFGs) is provide; namely $\beta-$product. We give sufficient conditions for the $\beta-$ product of two PFGs to be strong and we prove if the $\beta-$product of two PFGs is complete, then one of them is strong. We also study the unbiased notion of the class of PFGs and necessary and sufficient conditions for the $\beta-$product to be unbiased are given.