Research & Reviews: Discrete Mathematical Structures
Volume 9, Issue 1 (2022)
Published
Table of contents
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Vertex Covered Hypergraphs
Abstract: In this Paper I consider a minimal vertex covering sets and minimal strong vertex covering sets. I define Hypergraph, Sub-hypergraph, Partial sub-hypergraph, Vertex covering set, Minimal Vertex covering set, upper vertex covering set and upper vertex covering number in this paper and I consider the effect of removing a vertex on the upper vertex covering number of the hypergraph. Then I prove that the upper vertex covering number does not …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 9, Issue 1, 2022 · pp. 1–5 Read article
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Analysis Of Gradient Descent In Back Propagation Neural Network For Maximum And Efficient Utilization
Abstract: The back-propagation is a successfully established algorithm for multi-layered perceptron neural networks, which is usuallywith successfully for tiny network architectures or small tasks. In this paper we have highlighted the important libraries for thepurpose of implementation of neural networks. After that we have given the process of feed forward in neural network and howwe optimize this process by updating the weights by going backward towards the previous layers. The Author …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 9, Issue 1, 2022 · pp. 21–30 Read article
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Sum Divisor Cordial Labeling of Wheel Related Graph Families
Abstract: In this paper, we prove that the graphs obtained by switching of a rim in wheel Wn, switching of a vertex of degree 2 and 3 in gear graph Gn, switching of a vertex of degree 2 and 4 in flower graph fln, switching of a vertex of degree 2 and 3 in shell graph Sn are sum divisor cordial (SDC). A sum divisor cordial labeling (SDCL) of a graph …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 9, Issue 1, 2022 · pp. 31–39 Read article
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On Graph Theory Based on Matrix
Abstract: This paper presents a new approach of graph theory based on natural numbers and matrix only. The natural number is used for vertex and matrix for the edge. The fast graph generation is an advantage of this approach by the successor function. The connected and non-connected graph both is defined by the axiom. There is the arithmetic based on the additive and multiplicative operation over the matrix with the set …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 9, Issue 1, 2022 · pp. 40–46 Read article
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Projectivity of Universal Algebras
Abstract: The basic relations between universal algebras are homomorphisms and their special cases – monomorphisms, epimorphisms, and isomorphisms (cf., for example, (Kurosh, 1963; Cohn, 1965)). In this paper, we introduce and study a novel relation between universal algebras, which is called projectivity and allows obtaining properties of universal algebras from properties of those universal algebras to which they are weakly or finally projective. The key property of projectivity relations is that …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 9, Issue 1, 2022 · pp. 6–20 Read article