Volume-6 , Issue-3 , Jun 2019, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  About Pendent Inclusive Sets In Graphs

  D.K.Thakkar and N.J.Savaliya

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.128-135, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.128135

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  Abstract
  We introduce a new concept called pendent inclusive set in graphs. We also define maximum and 1-maximal pendent inclusive sets in graphs. We prove that for a graph G having a pendent vertex V(G) is the only maximum and 1-maximum pendent inclusive set of a graph. We prove a characterization of a 1-maximal pendent inclusive set of a graph can have at most ∆(G) pendent vertices. We also prove that if u and v have same degree. We further, prove that for any k_regular graph with K≥1, all 1-maximal pendent inclusive set have the same cardinality N-k+1. We also prove several results related to the effect of vertex removal and edge removal on pendent inclusive number of a graph.

  Key-Words / Index Term
  pendent inclusive set, maximum pendent inclusive set, maximal pendent inclusive set, k- dominating set, pendent edge, isolated edge

  References
  [1] D.K.Thakkar and N.J.Savaliya, “About Isolate Inclusive sets in Graphs “, International Journal of Mathematical And its Applications, Vol. 6, Issue 2-B, pp. 361-367, 2018.
  [2] D.K.Thakkar and N.J.Savaliya, “On Isolate Inclusive sets in Graphs “, International Journal of Innovation in Science and Mathematics, Vol. 5, Issue 3, pp. 74-76, 2017.
  [3] T.W.Haynes, S.T.Hedetniemi, P.J.Slater, “Fundamental of Domination In graphs”, Marcel Dekker, New York, 1998.
  [4] T.W.Haynes, S.T.Hedetniemi, P.J.Slater, “Domination In Graphs Advanced Topics”, Marcel Dekker, New York, 1998.

  Citation
  D.K.Thakkar and N.J.Savaliya, "About Pendent Inclusive Sets In Graphs," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.128-135, 2019

• Open Access   Article

  Clustering Using Finite Geometric Skew Normal Mixture Models

  Deepana R and Kiruthika C

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.136-143, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.136143

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  Finite mixtures of non-normal distributions using model based clustering approach have emerged as an effective tool in modeling heterogeneous data with asymmetric features. In particular, an attention is paid to the geometric skew normal mixture models which have been used for skewed data. Parameter estimation is carried out using Expectation Maximization (EM) algorithm. Euclidean distance based initialization technique is used for finding initial mixing proportion values. Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) are used to identify the optimal model. The clustering performance of these mixture models have been illustrated with the help of real and simulated datasets.

  Key-Words / Index Term
  Geometric skew normal distribution, Finite Mixture Model, Model based Clustering, EM algorithm.

  References
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  [17]. D. Kundu, “Geometric Skew Normal Distribution”, Sankhya: The Indian Journal of Statistics, Vol. 76, No. B, Issue. 2, pp.167-189, 2014.
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  Citation
  Deepana R and Kiruthika C, "Clustering Using Finite Geometric Skew Normal Mixture Models," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.136-143, 2019

• Open Access   Article

  Operations on Graphs and its Minimum Diameter Spanning Tree

  V.T. Chandrasekaran, N. Rajasri

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.144-148, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.144148

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  Abstract
  In this paper we present dominating sets, minimum diameter spanning tree for operations on graphs. We find out the minimum diameter spanning tree through the graph of which have a minimum diameter spanning tree such that both have same domination number. The spanning tree of the simple connected graph is said to be a minimum diameter spanning tree. if there is no other spanning tree ` of such that . The diameter of a graph is length of the shortest path between the most distance node.

  Key-Words / Index Term
  Domination, Diameter, Ladder graph, Grid graph, star graph, Path, Spanning tree, Cartesian product, co-normal product, lexico graphic product, and union, sum

  References
  [1] V.T Chandrasekaran, and N.Rajasri minimum diameter spanning tree, American journal of computational mathematics, 2018, 8, 203 – 208.
  [2] Michael S. Jacobson and Lael F. Kinch On the Domination of the Products of Graphs
  [3] S.Arumugam and S. Ramachandran, Invitation to Graph theory, copyright @2001 scitch puplications (india) pvt Ltd.
  [4] Haray, F. (1969) Graph Theory. Addsion Wesley, Reading, MA.
  https://doi.org/10.21236/AD0705364
  [5] P.Sharifani ,M.R Hooshmandasl and M.Alambardar Meybodi An explicit construction of optimal dominating and dominating sets in grid.arXiv:1707.0647v3[cs.DM] 2018
  [6] Samu Alanko, Simon Crevils, Andon Isopoussu, Patric Ostergard and Ville
  Pettersson computing the domination number of grid graphs. The Electronic Journal of Combinatorics 18(2011),# p141
  [7] SHEHID UR REHMAN, I.JAVAID. Fixing number of co normal product of graphs :https://www.reserachgate.net/publication/314182293.arXiv: 1703.00709V1.
  

  Citation
  V.T. Chandrasekaran, N. Rajasri, "Operations on Graphs and its Minimum Diameter Spanning Tree," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.144-148, 2019

• Open Access   Article

  The concept of Reneging and deferment in the arena of Queuing system

  S.K. Maragathasundari, S. Radha, N.Murugeswari

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.149-152, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.149152

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  Abstract
  This paper deals with a Queuing model in which an organization is rendered by systems for single server Also server squares whimsically in light of various reasons at the season of association. Here the association interruption occurs in the midst of the season of fundamental favorable position towards the clients. Fix procedure does not begin right away. A substantial postponement occurs in two phases before the initiation of patch up amidst the essential time of deferral, by virtue of uneasiness, the clients renege. Next amidst the second time of deferral, obliged sensibility knows about purpose of restriction the length of the line. For the above portrayed covering issue, the technique with state likelihood making inspiration driving choosing line length in the unequivocal packaging is settled utilizing profitable variable system. In like way the other execution degrees of the model are settled.

  Key-Words / Index Term
  Deferement, Reneging, Style, Revamp process

  References
  [1] Dhanalakshmi and S. Maragathasundari, “Mobile adhoc networks problem- A queueing approach”, International journal of communication networks and distributed systems, Vol.21, No.4, 2018.
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  [4] R. Kumar and S.K. Sharma, “A Markovian Feedback Queue with Retention of Reneged Customers and Balking”, AMO-Advanced Modeling and Optimization, Vol.14, No.3, pp.681-688, 2012.
  [5] R.F. Khalaf., K.C. Madan. & C.A. Lucas, “An M[x]/G/1 Queue with Bernoulli schedule, General vacation times, random breakdowns, general and general repair times”, Applied mathematical sciences,Vol.5, No.1,pp.35-51, 2011.
  [6] S. Maragathasundari and S. Srinivasa, “Analysis of M/G/1 feedback queue with three stage and multiple server vacation”, Applied mathematical sciences, Vol.6, No.125, pp.6221-6240, 2012.
  [7] S. Maragathasundari, “An examination on queuing system of general service Distribution with an establishment time and second discretionary administration”,Int. J. Appl. Comput. Math (2018) 4: 97. https://doi.org/10.1007/s40819-018-0529-3.(SPRINGER).
  [8] S. Shanthi Sivanandam, A. Muthu Ganapathi Subramanian and Gopal Sekar, “Transient analysis of single server queueing system with loss and feedback”, International Journal of Computer science and Engineering, Vol.07, Special issue.05, pp.270-274, 2019.
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  [10] V.P. Murugan, P.Sekar, “Queueing models using simulation method in busy mall”, International Journal of Computer science and Engineering, Vol.7, Issue. 5, pp.1431-1435, 2019.
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  Citation
  S.K. Maragathasundari, S. Radha, N.Murugeswari, "The concept of Reneging and deferment in the arena of Queuing system," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.149-152, 2019

• Open Access   Article

  Monitoring Process Mean and Variability Using Artificial Neural Networks

  S.M. Nimbale, V.B. Ghute

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.6 , Issue.3 , pp.153-158, Jun-2019

  CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.153158

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  Abstract
  In today`s modern market quality of product is most preferable parameter for customers. In order to fulfill the customer requirements manufacturing industries implementing the advanced technology in order to improve and maintain high quality of product. Consequently its real time need that process variation is to be controlled in very advanced approach.The Shewhart chart is usually used to monitor shifts in process mean, whereas, the R and S charts are most widely used in industry to monitor process variability. In this paper, artificial neural network based approach is developed for monitoring the mean and variability of the process. The ARL performance of the proposed approach is evaluated by using simulation and is compared with traditional Shewhart and S charts under normal process distribution. The proposed study indicates that ANN scheme is effective than and S charts for monitoring the process mean and variability.

  Key-Words / Index Term
  Artificial neural network; Statistical process control; X chart; S chart; Average run length

  References
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  Citation
  S.M. Nimbale, V.B. Ghute, "Monitoring Process Mean and Variability Using Artificial Neural Networks," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.3, pp.153-158, 2019