Volume-9 , Issue-5 , Oct 2022, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  A Study on Geo Chromatic Number of Some Graph Families

  U. Mary, R. Joseph Paul

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.5 , pp.1-6, Oct-2022

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  Abstract
  A proper coloring of a graph is that the allocate colors to the vertices of a graph in order that no two neighboring vertices have a similar color. The chromatic number is that the smallest number of colors needed to color G. The least cardinality among all the geodetic sets is known as geodetic number and is termed by g (G) and also the set C V (G) is termed as chromatic set if C contains all k-vertices of various colors in G, the least cardinality among all chromatic set is termed chromatic number and is denoted as . The synthesis of these concepts is termed Geo chromatic number . In this paper, we discuss about the Geo chromatic number of a Barbell graph, Helm graph, Gear Graph, Tadpole graph, Pan Graph, Lollipop graph, Bistar graph, Tristar graph, Web graph and Friendship graph are shown.

  Key-Words / Index Term
  Geodetic Number, Chromatic Number, Geo Chromatic Number

  References
  [1] A.Hansberg, L.Volkmann, “on the geodetic and geodetic domination number of graph”, Discrete Mathematics, Vol. 310, pp.2140 – 2146, 2010.
  [2] Arockia Aruldoss, G.Gurulakshmi, “The Dominator Coloring of Central and Middle Graph of Some Special Graphs”, International Journal of Mathematics and its Applications, Vol 4, Issue 4, pp.67 – 73, 2016.
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  [4] G. Chatrand, P. Zhang, “Introduction to Graph Theory” MacGraw Hill, 2005.
  [5] G. Chatrand, F. Harary, P. Zhang, “On the geodetic number of a graph’, Networks, Vol.39, Issue 1, pp.1-6, 2002.
  [6] G. Chatrand, F. Harary, P. Zhang, “Geodetic sets in graphs”, Discuss. Math., Graph Theory, Vol.20, Issue 1, pp.129-138, 2000.
  [7] J.A. Bondy and U.S.R. Murty, Graph Theory with Application, Macmilon Lonadon and Elsevier New York, 1976.
  [8] R. Joseph Paul, S. Beulah Samli, U. Mary, “A Study on Double Geo Chromatic Number of Line Graph of Some Graph Families,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.2, pp.7-11, 2022.
  [9] P.Suganya , R. Mary Jeya Jothi, “Dominator Chromatic Number of Some Garph Classes”, International Journal of Computational and Applied Mathematics, Vol 12, pp. 458 - 463, 2017.
  [10] S.B. Samli, S.R. Chellathurai, “Geo chromatic number of a graph’, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue 6, pp.259-264, 2018.
  [11] S. Beulah Samli, J. John, S. Robinson Chellathurai, “The Double Geo Chromatic Number of a graph”, Bulletin of the international Mathematical Virtual Institute, Vol.11, Issue 1, pp.25-38, 2021.

  Citation
  U. Mary, R. Joseph Paul, "A Study on Geo Chromatic Number of Some Graph Families," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.5, pp.1-6, 2022

• Open Access   Article

  Application of Inequalities for Finding Range of Non-elementary Integrals

  Toyesh Prakash Sharma

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.5 , pp.7-20, Oct-2022

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  This paper aims to use inequalities and functional inequality for approximating non-elementary integrals or finding nearby numerical values of non-elementary integrals without using advanced calculus and advanced functions like the error function, Incomplete gamma function, but for matching the values of those non-elementary integrals for some fixed lower and upper bound of it there we use Wolfram Alpha. for the better understanding reader should be aware of Cauchy-Schwarz Integral Inequality, Hermite-Hadamard Inequality for Convex functions, Hermite-Hadamard Inequality for Concave functions, Jensen`s Inequality for Concave and Convex function, Generalized Arithmetic-Geometric Mean Inequality etc.

  Key-Words / Index Term
  Elementary Integrals, non-elementary Inegrals, Closed Form, Upeer Bound and Lower Bound etc.

  References
  [1] Marchisotto, E.A. and Zakeri, G.A. An Invitation to Integration in Finite Terms. The College Mathematics Journal, Vol.25, pp.295-308. 1994.
  [2] G.H. Hardy, Littlewood, G. Pólya,” Inequalities.” Cambridge University Press, Cambridge pp.324, 1952.
  [3] S.P. Andriopoulos, A nice application of the Hermite–Hadamard inequality, Mathematical Spectrum Vol.47, Issue 2, p. 80–81, 2015.
  [4] Toyesh Prakash Sharma.: "A generalisation of the Arithmetic-Logarithmic-Geometric Mean Inequality, Parabola Magazine, Vol.58, No. 2, pp 1–5, 2022.
  [5] Nijimbere V “Evaluation of the non-elementary integral ?e?x?dx?e?x?dx, ??2??2, and other related integrals” Ural Math. J., Vol.3, no. 2. pp.130–142. 2017.
  [6] Rosenlicht M. “Integration in finite terms.” Amer. Math. Monthly , Vol.79, no. 9. P. 963–972, 1972.
  [7] Nijimbere V.” Evaluation of some non-elementary integrals involving sine, cosine, exponential and logarithmic integrals: Part II”. Ural Math. J, 2018.
  [8] Marchisotto, E.A. and Zakeri, G.A. An Invitation to Integration in Finite Terms. The College Mathematics Journal,Vol.25, pp.295-308. 1994.

  Citation
  Toyesh Prakash Sharma, "Application of Inequalities for Finding Range of Non-elementary Integrals," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.5, pp.7-20, 2022

• Open Access   Article

  On The Modification of Adomian Decomposition Method for the Solution of Linear and Non-Linear Lane-Emden Equation

  Kanee Goodfaith Leyira, N.H. Manjak, A.G. Madaki, Okai O. Jeremiah

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.5 , pp.21-30, Oct-2022

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  The main aim of this study, to develop a new modification for solving Lane-Emden and Emden-Fowler Equation based on the Adomian Decomposition Method (ADM). In particular, we focused on the Lane-Emden Equation. The modification is void of the difficulty and complexity of calculating the Adomian polynomials for high nonlinear part and also to address the singularity of the equation. While the Adomian Decomposition Method (ADM) uses the Adomian polynomials to approximate the nonlinear unknown function, our modification introduces the successive approximation method into the traditional Adomian Decomposition Method (ADM). This procedure frees us from the Adomian polynomials calculations and integrations in terms of the linear case. Furthermore, the proposed method gives the series solutions directly. An experiment was performed on the problems with known exact solutions. The approximate solutions obtained by the modifications were compared to the exact solutions and other methods for evaluating the accuracy. It was found that we can predict the closed form solutions within a few terms of the series solutions in almost our entire Examples. The new method is more efficient and have several advantages over some of the existing analytical methods.

  Key-Words / Index Term
  The main aim of this study, to develop a new modification for solving Lane-Emden and Emden-Fowler Equation based on the Adomian Decomposition Method (ADM). In particular, we focused on the Lane-Emden Equation. The modification is void of the difficulty and complexity of calculating the Adomian polynomials for high nonlinear part and also to address

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  Citation
  Kanee Goodfaith Leyira, N.H. Manjak, A.G. Madaki, Okai O. Jeremiah, "On The Modification of Adomian Decomposition Method for the Solution of Linear and Non-Linear Lane-Emden Equation," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.5, pp.21-30, 2022

• Open Access   Article

  On About the Applications of Topological Sets and Space to Some Field of Studies

  Kanee Goodfaith Leyira, Isah Abdullahi, Mahmud Musa, Salisu Haruna, Ali Musa, Abdulrahim Hindatu, Mohammed Adamu

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.5 , pp.31-33, Oct-2022

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  Abstract
  In this study, we discuss some applications of general topology to science, engineering, business, medicine and technology. We presented key ideas to the applicability of closed set and the space, their properties and connection to different spaces and capacities to these other fields of studies. Topology being one of the most important branches of pure mathematics has influenced the whole world with so strong effects and incredible applications.

  Key-Words / Index Term
  Topology, Geometry, Sets, Space, Limit Point, Neighborhood, Generalization

  References
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  Citation
  Kanee Goodfaith Leyira, Isah Abdullahi, Mahmud Musa, Salisu Haruna, Ali Musa, Abdulrahim Hindatu, Mohammed Adamu, "On About the Applications of Topological Sets and Space to Some Field of Studies," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.5, pp.31-33, 2022

• Open Access   Article

  Comparative study on Type I, Type II and gestational Diabetes Patients Using a Weighted Power Prakaamy Distribution

  Arumugam P., Arulmozhi V.

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.9 , Issue.5 , pp.34-45, Oct-2022

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  Abstract
  In the current study, a novel model of power prakaamy distribution known as the weighted power prakaamy distribution has been examined. Moments, Order statistics, the Likelihood Ratio test, entropies, the Bonferroni and Lorenz curves, and other statistical properties of the proposed distribution have been computed and analysed. The parameters of the new distribution are examined using the (MLE) maximum likelihood estimator, and the (FIM) Fisher`s information matrix has been addressed. The Weighted Power prakaamy distribution used in Type I, Type II and Gestational Diabetes datasets. In this paper, we have to study on these three types of diabetes and we will find out, which one is mostly affected and then which age group of people mostly affected in of diabetes. Finally, Comparative study on this distribution is executed to show its flexibility and superiority over other distributions.

  Key-Words / Index Term
  Diabetes mellitus, Weighted Power Prakaamy distribution, Survival analysis, Moment, Maximum likelihood estimation.

  References
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  Citation
  Arumugam P., Arulmozhi V., "Comparative study on Type I, Type II and gestational Diabetes Patients Using a Weighted Power Prakaamy Distribution," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.5, pp.34-45, 2022