This article is devoted to the determination of edge-based eccentric topological indices of a zero divisor graph of some algebraic structures. In particular, we computed the first Zagreb eccentricity index, third Zagreb eccentricity index, geometric-arithmetic eccentricity index, atom-bond connectivity eccentricity index and a fourth type of eccentric harmonic index for zero divisor graphs associated with a class of finite commutative rings.
In this paper, n-ary block codes for KU-algebras and their interconnecting properties in terms of block codes have been given. A construction of n-ary block codes for a given KU-algebra is shown, and it is proved that for each n-ary block code K we can associate a KU-algebra X, such that the constructed n-ary block codes generated by X, i.e. K x , contain the code K as a subset. We have proved that for every n-ary block-code K, there exists a KU-valued function on a KU-algebra which determines K. It is also shown that the KU-algebras associated with an n-ary block code are not unique up to isomorphism. ARTICLE HISTORY KEYWORDS KU-algebra; n-ary block codes; generalized cut functions 2010 MATHEMATICS SUBJECT CLASSIFICATIONS 06F35; 03G25 Definition 2. 1 ([1]): By a KU-algebra we mean an algebra (X, •, 1) of type (2, 0) with a single binary operation • that satisfies the following identities: for any x, y, z ∈ X,
In this paper, we prove that the n-simple braid divisible by the generators xi for all 2 ≤ i ≤ n-2 has trivial simple centralizer. Consequently, the commuting graph defined on the set of simple braids is disconnected. We also prove that the graph has one major component.
<abstract><p>In this paper, we have discussed quotient structures of KU-algebras by using the concept of intersection soft ideals. In general, the soft sets are parameterized families of sets that are used to dealt with uncertainty. In particular, We have given the fundamental homomorphism theorem of quotient KU-algebras. A characterization of commutative quotient KU-algebras, implicative quotient KU-algebras and positive implicative quotient KU-algebras are also presented.</p></abstract>
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