ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

#### For citation:

Ganesamoorthy K., Lakshmi Priya S. Forcing total outer connected monophonic number of a graph. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2022, vol. 22, iss. 3, pp. 278-286. DOI: 10.18500/1816-9791-2022-22-3-278-286, EDN: IMTPKR

Published online:
31.08.2022
Full text: download
Language:
English
Article type:
Article
UDC:
519.17
EDN:
IMTPKR

# Forcing total outer connected monophonic number of a graph

Autors:
Ganesamoorthy Kathiresan, Coimbatore Institute of Technology
Lakshmi Priya Shanmugam, CIT Sandwich Polytechnic College
Abstract:

For a connected graph $G = (V,E)$ of order at least two, a subset $T$ of a minimum total outer connected monophonic set $S$ of $G$ is a forcing total outer connected monophonic subset for $S$ if $S$ is the unique minimum total outer connected monophonic set containing $T$. A forcing total outer connected monophonic subset for $S$ of minimum cardinality is a minimum forcing total outer connected monophonic subset of $S$. The forcing total outer connected monophonic number $f_{tom}(S)$ in $G$ is the cardinality of a minimum forcing total outer connected monophonic subset of $S$. The forcing total outer connected monophonic number of $G$ is $f_{tom}(G) = \min\{f_{tom}(S)\}$, where the minimum is taken over all minimum total outer connected monophonic sets $S$ in $G$.  We determine bounds for it and find the forcing total outer connected monophonic number of a certain class of graphs.  It is shown that for every pair $a,b$ of positive integers with $0 \leq a < b$ and $b \geq a+4$, there exists a connected graph $G$ such that $f_{tom}(G) = a$ and $cm_{to}(G) = b$, where $cm_{to}(G)$ is the total outer connected monophonic number of a graph.

Key words:
Acknowledgments:
The first author's research work was supported by National Board for Higher Mathematics (NBHM), Department of Atomic Energy (DAE), Government of India (project No. NBHM/R.P.29/2015/Fresh/157).
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