TY - JOUR
ID - 14268
TI - Extreme outer connected monophonic graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - K., Ganesamoorthy
AU - S, Lakshmi Priya
AD - Department of Mathematics, Coimbatore Institute of Technology
(Government Aided Autonomous Institution)
Coimbatore - 641 014, India
AD - Department of Mathematics, Coimbatore Institute of Technology, Coimbatore
Y1 - 2022
PY - 2022
VL - 7
IS - 2
SP - 211
EP - 226
KW - outer connected monophonic set
KW - outer connected monophonic number
KW - extreme order
KW - extreme outer connected monophonic graph
DO - 10.22049/cco.2021.27042.1184
N2 - For a connected graph $G$ of order at least two, a set $S$ of vertices in a graph $G$ is said to be an \textit{outer connected monophonic set} if $S$ is a monophonic set of $G$ and either $S=V$ or the subgraph induced by $V-S$ is connected. The minimum cardinality of an outer connected monophonic set of $G$ is the \textit{outer connected monophonic number} of $G$ and is denoted by $m_{oc}(G)$. The number of extreme vertices in $G$ is its \textit{extreme order} $ex(G)$. A graph $G$ is said to be an \textit{extreme outer connected monophonic graph} if $m_{oc}(G)$ = $ex(G)$. Extreme outer connected monophonic graphs of order $p$ with outer connected monophonic number $p$ and extreme outer connected monophonic graphs of order $p$ with outer connected monophonic number $p-1$ are characterized. It is shown that for every pair $a, b$ of integers with $0 \leq a \leq b$ and $b \geq 2$, there exists a connected graph $G$ with $ex(G) = a$ and $m_{oc}(G) = b$. Also, it is shown that for positive integers $r,d$ and $k \geq 2$ with $r < d$, there exists an extreme outer connected monophonic graph $G$ with monophonic radius $r$, monophonic diameter $d$ and outer connected monophonic number $k$.
UR - http://comb-opt.azaruniv.ac.ir/article_14268.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14268_9a46437c0806e08d6d1d2388dd680b82.pdf
ER -