Forcing total outer connected monophonic number of a graph
| Autor: | Ganesamoorthy, Kathiresan, Lakshmi Priya, Shanmugam |
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| Jazyk: | English<br />Russian |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика, Vol 22, Iss 3, Pp 278-286 (2022) |
| Druh dokumentu: | article |
| ISSN: | 1816-9791 2541-9005 |
| DOI: | 10.18500/1816-9791-2022-22-3-278-286 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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