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Monophonic eccentric domination in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 2، دوره 9، شماره 4، اسفند 2024، صفحه 625-633 اصل مقاله (393.29 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28156.1460 | ||
| نویسندگان | ||
| Titus P.* 1؛ Ajitha Fancy J.2 | ||
| 1Department of Mathematics, University College of Engineering Nagercoil, Anna University, Tirunelveli Region, Nagercoil - 629 004, India | ||
| 2Department of Mathematics, Scott Christian College (Autonomous), Nagercoil - 629 003, India | ||
| چکیده | ||
| For any two vertices $u$ and $v$ in a connected graph $G,$ the monophonic distance $d_m(u,v)$ from $u$ to $v$ is defined as the length of a longest $u-v$ monophonic path in $G$. The monophonic eccentricity $e_m(v)$ of a vertex $v$ in $G$ is the maximum monophonic distance from $v$ to a vertex of $G$. A vertex $v$ in $G$ is a monophonic eccentric vertex of a vertex $u$ in $G$ if $e_m(u) = d_m(u,v)$. A set $S \subseteq V$ is a monophonic eccentric dominating $set$ if every vertex in $V-S$ has a monophonic eccentric vertex in $S$. The monophonic eccentric domination number $\gamma_{me}(G)$ is the cardinality of a minimum monophonic eccentric dominating set of $G$. We investigate some properties of monophonic eccentric dominating sets. Also, we determine the bounds of monophonic eccentric domination number and find the same for some standard graphs. | ||
| کلیدواژه‌ها | ||
| monophonic path؛ monophonic distance؛ monophonic eccentric vertex؛ monophonic eccentric dominating set؛ monophonic eccentric domination number | ||
| مراجع | ||
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