The Outer Connected Detour Monophonic Number of a Graph

Authors

  • N.E Johnwin Beaula Research Scholar. Scott Christian College (Autonomous), Nagercoil – 629003, India
  • S Joseph Robin Department of Mathematics, Scott Christian College (Autonomous), Nagercoil – 629003, India

DOI:

https://doi.org/10.23755/rm.v44i0.921

Keywords:

chord, monophonic path, monophonic number, detour monophonic path, detour monophonic number, outer connected detour monophonic number

Abstract

For a connected graph ???? = (????, ????) of order  a set is called a monophonic set of ????if every vertex of ????is contained in a monophonic path joining some pair of vertices in ????. The monophonic number (????) of is the minimum cardinality of its monophonic sets. If  or the subgraph  is connected, then a detour monophonic set  of a connected graph is said to be an outer connected detour monophonic setof .The outer connecteddetourmonophonic number of , indicated by the symbol , is the minimum cardinality of an outer connected detour monophonic set of . The outer connected detour monophonic number of some standard graphs are determined. It is shown that for positive integers , and ???? ≥ 2 with ,there exists a connected graph ????with???????????????????? = , ????????????m???????? = and  = ????. Also, it is shown that for every pair of integers ????and b with 2 ≤ ???? ≤ ????, there exists a connected graph with and .

References

T. W. Haynes, S. T. Hedetniemi and P. J, Slater, Fundamentals Of Domination In Graphs, Marcel Dekker, New York, (1998).

J. John, The Forcing Monophonic And The Forcing Geodetic Numbers Of A Graph, Indonesian Journal of Combinatorics 4(2), (2020), 114-125.

J. John and S. Panchali 2, The upper monophonic number of a graph, Int. J. Math.Combin. 4, (2010),46 – 52.

P. Titus, K. Ganesamoorthy and P. Balakrishnan, The Detour Monophonic Number of A Graph. J. Combin. Math. Combin. Comput., (84), (2013),179-188

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Published

2022-12-11

Issue

Vol. 44 (2022): Special Issue: Recent Trends in Mathematics and its Applications

Section

Volume 45-2023

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