The Path Induced Edge-to-Vertex Monophonic Number of Graphs

I. Annalin Selcy; P. Arul Paul Sudhahar; S. Robinson Chellathurai

doi:https://doi.org/10.14445/22315373/IJMTT-V66I8P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 8 | Year 2020 | Article Id. IJMTT-V66I8P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I8P509

The Path Induced Edge-to-Vertex Monophonic Number of Graphs

I. Annalin Selcy, P. Arul Paul Sudhahar, S. Robinson Chellathurai

Abstract

Let G be a connected graph with at least three vetices. An edge-to-vertex monophonic set is called a path induced edge-to-vertex monophonic set of G if contains a Hamiltonian path. The minimum cardinality of a path induced edge-to-vertex monophonic set is called the path induced edge-to-vertex monophonic number of G and is denoted by pimev(G). The minimum path induced edge-to-vertex monophonic set with |M|=pimev(G) is called a minimum path induced ege-to-vertex monophonic number of G or pimev-set of G. Some general properties satisfied by this concept are studied. For every pair a and b of integers with 4≤a≤b, there exists a connected path induced edge-to-vertex geodetic graph G such that pimev(G) a and pigev(G) =b.

Keywords

monophonic path, monophonic number, path induced edge-to-vertex monophonic number.

References

[1] Arul Asha and S. Joseph Robin, International Journal of Scientific Research and Reviews, Path Induced Geodesic Graphs, 8(2) (2019), 1-8.
[2] Buckley. F and Harary. F, Distance in Graphs, Addison-Wesley, Redwood City, CA, 1990.
[3] John, J & Uma Samundeswari, K 2012, ‘The edge-to- vertex Monophonic number of a graph’, International Journal of Mathematical Archive, vol. 3, no. 2, pp. 722-728 .
[4] Ruthlyn N. Villarante And Imelda S. Aniversario, Path-Induced Geodetic Numbers of Some Graphs, Journal of ultra scientist of Physical Sciences, 29(5), (2017),196- 204.
[5] Santhakumaran, P & John, J 2012, ‘On the edge-to- vertex geodetic number of a graph’, Miskolc Mathematical Notes, vol. 13, no. 1, pp. 107-119.

Citation :

I. Annalin Selcy, P. Arul Paul Sudhahar, S. Robinson Chellathurai, "The Path Induced Edge-to-Vertex Monophonic Number of Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 8, pp. 82-91, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I8P509