On The Strong Edge Monophonic Number of Graphs

Authors

  • Xavier DA Department of Mathematics, Loyola College, Chennai
  • Infanta LG Department of Mathematics, Loyola College, Chennai

Keywords:

Monophonic set, Strong monophonic set, Edge monophonic set, Monophonic distance

Abstract

Abstract For a connected graph of order at least two, a set of vertices of is a Strong edge Monophonic set if every edge of is contained in a fixed monophonic path between any pair of vertices of . The minimum cardinality of the strong edge monophonic set is the strong edge monophonic number of denoted my . In this paper, certain general properties of the strong edge monophonic sets are studied. Also the strong monophonic number of some families of graph are determined

References

[1] Harary, Frank, Emmanuel Loukakis, and Constantine Tsouros. "The geodetic number of a graph." Mathematical and Computer Modelling 17.11 (1993): 89-95.

[2] Santhakumaran, A. P., P. Titus, and K. Ganesamoorthy. "On the monophonic number of a graph." Journal of applied mathematics and informatics 32.1-2 (2014): 255-266.

[3] Hernando, Carmen, et al. "On monophonic sets in graphs." Submitted. Google Scholar (2005).

[4] Iršič, Vesna. "Strong geodetic number of complete bipartite graphs and of graphs with specified diameter." Graphs and Combinatorics 34.3 (2018): 443-456.

[9] Manuel, Paul, et al. "Strong geodetic problem in networks: computational complexity and solution for Apollonian networks." arXiv preprint arXiv:1708.03868 (2017).

[6] Klavžar, Sandi, and Paul Manuel. "Strong Geodetic Problem in Grid-Like Architectures." Bulletin of the Malaysian Mathematical Sciences Society (2018): 1-10.

[7] Iršič, Vesna, and Sandi Klavžar. "Strong geodetic problem on Cartesian products of graphs." RAIRO-Operations Research 52.1 (2018): 205-216.

[8] John, J., and P. Arul Paul Sudhahar. "On the edge monophonic number of a graph." Filomat 26.6 (2012): 1081-1089.

[9] Manuel, Paul, et al. "Strong edge geodetic problem in networks." Open Mathematics 15.1 (2017): 1225-1235.

[10] D.Antony Xavier and Elizabeth Thomas. “On the strong monophonic number of a graph.” (To appear)

Downloads

Published

2025-11-25

How to Cite

[1]
D. A. Xavier and B. L. Infanta, “On The Strong Edge Monophonic Number of Graphs”, Int. J. Comp. Sci. Eng., vol. 7, no. 5, pp. 20–24, 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.