Induced P_3-Packing k-partition Number for Certain Graphs

Authors

  • Antony Xavier Department of Mathematics, Loyola College, Chennai 600 034, India
  • Santiagu Theresa Department of Mathematics, Loyola College, Chennai 600 034, India
  • S. Maria Jesu Raja Raja Department of Mathematics, Loyola College, Chennai 600 034, India

Keywords:

Perfect, Perfectpacking, Almost Perfect, -packing, Induced, partition, Butterfly networks, Honeycomb Networks and Circum Pyrene

Abstract

Finding a partition V_1,V_2,...,V_k of V(G) with minimum k is called the induced H-packing k-partition problem of G. The minimum induced H-packing k-partition number is denoted by ipp(G,H). In this paper we determine an induced P_3-packing k-partition number for Butterfly Networks, Honeycomb Networks, and Circum Pyrene with H is isomorphic to P_3.

References

[1] A. Al Mutairi, Bader Ali and D. Paul Manuel, "Packing in Carbon Nanotubes", Journal of Combinatorial Mathematics and Combinatorial Computing , 92, 2015, 195 - 206.

[2] R. Bar-Yehuda, M. Halldorsson, J. Naor, H. Shachnai and I. Shapira, "Scheduling split intervals", in: Proc. Thirteenth Annu. ACM - SIAM Symp, 2002,732 - 741.

[3] R. Bejar, B. Krishnamachari, C. Gomes and B. Selman, "Distributed constraint satisfaction in a wireless sensor tracking system", Workshop on Distributed Constraint Reasoning, Internat. Joint Conf. on Artificial Intelligence, 2001.

[4]A. Felzenbaum, "Packing lines in a hypercube", Discrete Mathematics 117, 1993, 107 - 112.

[5] P. Hell and D. Kirkpatrick, "On the complexity of a generalized matching problem", in: Proc. Tenth ACM Symp, 1978, 309 - 318.

[6] A. Muthumalai, I. Rajasingh and A. S. Shanthi, "Packing of Hexagonal Networks", Journal of Combinatorial Mathematics and Combinatorial Computation, 79, 2011, 121 - 127.

[7] D. Paul Manuel, I. Mostafa Abd-El-Barr, I. Rajasingh, Bharati Rajan, "An efficient representation of Benes networks and its applications", Journal of Discrete Algorithms, 6, 2008, 11 - 19.

[8] J. Quadras, K. Balasubramanian, K.A. Christy, "Analytical expressions for Wiener indices of n-circumscribed peri-condensed benzenoid graphs", Journal of Mathematical Chemistry, 54, 2016, 823 - 843.

[9] S.M.J. Raja, A. Xavier, I. Rajasingh, "Induced H-packing k-partition problem in interconnection networks", International Journal of Computer Mathematics: Computer Systems Theory. 2, 2017 136 - 146.

[10] I. Rajasingh, A. Muthumalai, R. Bharati and A. S. Shanthi, "Packing in honeycomb networks", Journal of Mathematical Chemistry, 50, 5, 2012, 1200 - 1209.

[11] H. Liu, L. Xie, J. Liu, L. Ding, "Application of Butterfly Clos-Network in Network-on-Chip", The Scientific World Journal, 2014, 1–11.

Downloads

Published

2025-11-25

How to Cite

[1]
A. Xavier, S. Theresal, and S. M. J. R. Raja, “Induced P_3-Packing k-partition Number for Certain Graphs”, Int. J. Comp. Sci. Eng., vol. 7, no. 5, pp. 91–95, Nov. 2025.

Issue

Vol. 7 No. 5 (2019): IJCSE Special Issue Mar Edition

Section

Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors contributing to this journal agree to publish their articles under the Creative Commons Attribution 4.0 International License, allowing third parties to share their work (copy, distribute, transmit) and to adapt it, under the condition that the authors are given credit and that in the event of reuse or distribution, the terms of this license are made clear.