Research & Reviews: Discrete Mathematical Structures
Volume 6, Issue 1 (2019)
Published
Table of contents
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Commutativity of Some Graph Operators
Abstract: AbstractThe line graph L(G) of a graph G has the edges of G as its vertices and two distinct edges of G are adjacent in L(G) if they are incident in G. In this paper we consider the commutativity of the line graph operator with some other operators such as Gallai graph Γ(G), anti- Gallai graph Δ(G), kth power of a graph Powk(G), k-distance graph Tk(G), cycle graph Cy(G), block …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 1, 2019 · pp. 1–5 Read article
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On Generalized fractional Integral Operators
Abstract: AbstractIn this paper, different integral operators for functions of two variables namely fractional integral operator and generalized fractional integral operator have been defined. Also defined the different spaces for functions of two variables and studied defined the operators on these spaces. Finally, proved the generalized fractional integral operators for function of two variables that are bounded from a generalized Morrey space of functions of two variables to another.Keywords: fractional integral …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 1, 2019 · pp. 10–14 Read article
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On the Pendant Number of Some New Graph Classes
Abstract: AbstractA decomposition of a graph is a collection of its edge disjoint sub-graphs such that their union is . If all the sub-graphs in the decomposition are paths, then it is a path decomposition. In this paper, we discuss the pendant number, the minimum number of end vertices of paths in a path decomposition of a graph. We also determine this parameter for some graph classes.Keywords: Decomposition, path decomposition, pendant …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 1, 2019 · pp. 15–21 Read article
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Resolving Travelling Salesman Problem Using Modified Clustering Technique
Abstract: AbstractTravelling Salesman Problem (TSP) is a quotidian stumbling block in the field of Computer Science and operation research designed to seek out the shortest pathway amid the given targets viz. cities where each target is considered only once. Many solutions to this setback like Ant Colony Optimization. Brute-Force approach, Genetic Algorithm, Fruit Fly Optimization etc. are available in literature. The main objective of these solutions is to minimize the time …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 1, 2019 · pp. 22–31 Read article
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n-Dimensional Eigenfunction Wavelet Transform
Abstract: AbstractIn this paper, Eigenfunction transform defined for single variable is extended for functions of n variables. Translation, convolution and dilation associated with n dimensional Eigenfunction transform are defined. Also, we define Eigenfunction wavelet for n variables. Eigenfunction wavelet transform (EWT) for n variables is introduced. Inversion formula for n dimensional EWT is also derived. Keywords: Eigenfunction transform Eigenfunction wavelet transform, translation, convolution, dilationCite this ArticleT.G. Thange, R.D. Swami, A.M.Alure. n-Dimensional …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 1, 2019 · pp. 32–37 Read article
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Fractional q-Derivative and Generalized N2 Function
Abstract: AbstractThis paper is devoted to fractional q-derivative of special functions. To begin with the theorem on term by term q-fractional differentiation has been derived. The result is an extension of an earlier result due to Yadav and Purohit and Sharma, Jain and Ali. As a special case, of fractional q-differentiation of N2 Function has been obtained.Keywords: Fractional integral and derivative operators, Fractional q-derivative, N2 Function and Special functionsMathematics Subject Classification: …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 1, 2019 · pp. 38–40 Read article
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Fractional q-Derivative and N2 Function
Abstract: AbstractThe study of fractional q-calculus in this paper serves as a bridge between the fractional q-calculus in the literature and the fractional q-calculus of Special Functions. This paper is devoted to fractional q-derivative of special functions. Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, physics, or other applications in engineering .To begin with the theorem on …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 1, 2019 · pp. 41–43 Read article
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FRACTIONAL q-DERIVATIVE AND GENERALIZED K-FUNCTION
Abstract: AbstractThis investigation is basically intended to fractional q-derivative of special functions. In this article we drive the results on term by term q-fractional differentiation of a generalized k-Series. As particular case we will obtain the fractional q-differentiation of the power series and exponential series. To start with the theorem on term by term q-fractional differentiation has been derived. The result is an extension of an earlier result due to Yadav …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 1, 2019 · pp. 6–9 Read article