Boolean expression based on hypergraphs with algorithm

Document Type : Research Paper


1 Department of mathematics, Payame Noor university, Tehran, Iran.

2 Department of Mathemtics, Payame Noor University, Tehran, Iran



This paper  introduces a novel concept of  Boolean function--based hypergraph  with respect to any given T.B.T(total binary truth table). This study defines a notation of  kernel set   on  switching functions and proves  that every  T.B.T corresponds to a  Minimum   Boolean expression via  kernel set  and presents  some conditions on  T.B.T to obtain  a Minimum irreducible   Boolean expression from switching functions. Finally, we present an algorithm and so Python programming(with complete and original codes) such that for any given T.B.T, introduces a Minimum irreducible   switching expression.


[1] C. Berge, Graphs and Hypergraphs, North Holland, 1979.
[2] P. Chandra R. K. Singh, Y., Generation of mutants for boolean expression, J. Discrete Math. Sci. Cryptogr., (2014), pp. 589-607.
[3] J. Eldon Whitesitt, Boolean Algebra and Its Applications, New York Dover Publications, Inc., 1995.
[4] M. Hamidi, A. Borumand saied, Accessible single-valued neutrosophic graphs, J. Appl. Math. Comput., Vol. 57 (2018), pp. 121-146.
[5] M. Hamidi, A. Borumand saied, Achievable Single-Valued Neutrosophic Graphs in Wireless Sensor Networks, New Math. Nat. Comput., Vol. 14 No. 2 (2018), pp. 157-185.
[6] M. Hamidi and A. Borumand Saeid, On Derivable Trees, Trans. Combin., Vol. 8 N. 2 (2019), pp. 21-43.
[7] M. Hamidi and F. Smarandache, Single-Valued Neutrosophic Directed (Hyper)Graphs And Applications in Networks, J. Intell. Fuzzy. Syst., Vol. 37 N. 2 (2019), pp. 2869-2885.
[8] M. Hamidi and R. Ameri, -Derivable Digraphs and its Application in Wireless Sensor Networking, Discrete. Math. Algorithms. Appl., (2020).
[9] B. Molnar, Applications of Hypergraphs in Informatics a Survey and Opportunities for Research, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 42 (2014), pp. 261-282.
[10] F. Smarandache, Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical-/Neutro-/Anti-) HyperAlgebra, Neutrosophic Sets
and Systems, Vol. 33 (2020), pp. 290-296.
[11] F. Smarandache, n-SuperHyperGraph and Plithogenic n-SuperHyperGraph, in Nidus Idearum, Vol. 7, second
edition, Pons asbl, Bruxelles, pp. 107-113, 2019;