The Outer Connected Detour Monophonic Number of a Graph

N.E Johnwin Beaula, S Joseph Robin

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 .


Keywords


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

Full Text:

PDF

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




DOI: http://dx.doi.org/10.23755/rm.v44i0.921

Refbacks

  • There are currently no refbacks.


Copyright (c) 2022 N.E Johnwin Beaula, S Joseph Robin

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

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.