Independent Monophonic Sets in Graphs

  • A Sadiquali M. E. A Engineering College, Perinthalmanna
  • P. Arul Paul Sudhahar Rani Anna Government College for Women, Tirunelveli
Keywords: Chordless Path, Monophonic Number, Independence Number, Geodetic Number, Independent Monophonic Number, Outer Independent Monophonic Number

Abstract

In this paper, we obtain two variables for the connected (p,q)-graphs G which is the minimum size of an independent monophonic set and an outer independent
monophonic set of G, termed as an independent monophonic number and an outer independent monophonic number of the connected (p,q)-graphs G, respectively.

Author Biographies

A Sadiquali, M. E. A Engineering College, Perinthalmanna

M. E. A Engineering College, Perinthalmanna, Kerala, India.

P. Arul Paul Sudhahar, Rani Anna Government College for Women, Tirunelveli

Rani Anna Government College for Women, Tirunelveli, Tamilnad, India.

References

P. A. P. Sudhahar, A. Sadiquali, and M. M. A. Khayyoom, “The Monophonic Geodetic Domination Number of Graphs,” Journal of Comp. Math. Sci., vol. 7, no. 1, 2016, pp. 27-38. www.compmath-journal.org

F. Buckley, and F. Harary, Distance in Graphs Addition Wesley, Redwood City, 1990.

G. Chatrand, and P.Zhang: Introduction to Graph theory, Tata mcGraw-Hill Publishing Company Ltd., 2006.

G. Chartrand, F. Harary, and P. Zhang, “On the Geodetic Number of a Graph,” Networks, pp 1-6, 2002.

E. M . Paluga, S. R. Canoy, Jr., “Monophonic Numbers of the Join and Composition of Connected Graphs,” Discrete Mathematics, vol. 307, pp. 1146-1154, 2007, doi.org/10.1016/j.disc.2006.08.002.

W. Goddard, and M. A. Henning. “Independent domination in graphs: A survey and recent results,” Discrete Mathematics, vol. 313, no. 7, pp. 839-854, 2013, doi.org/10.1016/j.disc.2012.11.031.

F. Harary, Graph Theory, Addition Wesley, 1969.

F. Harary, E. Loukakis, and C. Tsouros, “The Geodetic Number of a Graph,” Math. Comput. Modeling, vol. 11, pp. 89-95, 1993.

C. Hernando, T. Jiang, M. Mora, I. M. Pelayo, C. Seara, “On the Steiner, Geodetic and Hull Numbers of Graphs,” Discrete Mathematics, vol. 293, pp. 139-154, 2005. doi.org/10.1016/j.disc.2004.08.039

J. John and P. A. P. Sudhahar, “On The Edge Monophonic Number of a Graph,” Filomat, vol. 26, no. 6. pp. 1081-1089, 2012.

J. John, P. A. P. Sudhahar, and A. Vijayan, “The Connected Monophonic Number of a Graph,” International Journal of Combinatorial Graph Theory and Applications, vol. 5, no. 1, pp. 83- 90, 2012.

J. John, and S. Panchali, “The upper monophonic number of graph,” Int. Journal .of mathematics and Combinatorics, vol. 4, pp. 46-52, 2010.

F. S. Roberts, Graph Theory and Its Applications to Problems of Society, SIAM, Philadelphia, 1978, pp. 57-64.

N. J. Rad, and L. Volkmann. “A note on the independent domination number in graphs,” Discrete Applied Mathematics, vol. 161, no. 18, pp. 3087-3089, 2013. doi.org/10.1016/j.dam.2013.07.009

A. Sadiquali, and P. A. P. Sudhahar, “Bounds for Monophonic Domination Sum of a Graph and its ComplementA Nordhaus-Gaddum Approach,” Applied Mathematical Sciences, vol. 11, no. 60, pp. 2995-3005, 2017, doi.org/10.12988/ams.2017.79291

A. Sadiquali, and P. A. P. Sudhahar, “Monophonic Domination in Special Graph Structures and Related Properties,” International Journal of Mathematical Analysis, vol. 11, no. 22, pp. 1089-1102, 2017, doi.org/10.12988/ijma.2017.79125

A. Sadiquali, and P. A. P. Sudhahar, “Upper Monophonic Domination Number of a Graph” Int. Journal of Pure and App. Math. Special, vol. 120, no. 7, pp. 165-173, 2018. www.acadpubl.eu/hub/

A. Sadiquali, and P. A. P. Sudhahar, “A face change of Monophonic Dominating Sets by non-adjacency in Graphs,” International Journal of Innovative Technology and Exploring Engineering, vol. 8, no. 7, 2019, www.ijitee.org

A. P Santhakumaran, P. Titus, and R. Ganesamoorthy, “On The Monophonic Number of a Graph,” Applied Math and Informatics, vol. 32, pp. 255-266, 2014, doi.org/10.14317/jami.2014.255.

A. P. Santhakumaran, and P. Titus, “Monophonic Distance in Graphs,” Discrete Mathematics Algorithms and Applications, vol. 2, pp. 159-269, 2011, doi.org/10.1142/S1793830911001176.

T. A. Mangam, J. V. Kureethara -"Diametral paths in total graphs of complete graphs, complete bipartite graphs and wheels" Int. J. Civil Eng. Tech, vol. 8, no. 5, 2017

Published
2019-07-01
Section
Research Articles