Detour Monophonic Graphoidal Covering Number of Corona Product Graph of Some Standard Graphs with the Wheel

Abstract

A chord of a path $P$ is an edge joining two non-adjacent vertices of $P$. A path $P$ is called a monophonic path if it is a chordless path. A longest $x-y$ monophonic path is called an $x-y$ detour monophonic path. A detour monophonic graphoidal cover of a graph $G$ is a collection $psi_{dm}$ of detour monophonic paths in $G$ such that every vertex of $G$ is an internal vertex of at most one detour monophonic path in $psi_{dm}$ and every edge of $G$ is in exactly one detour monophonic path in $psi_{dm}$. The minimum cardinality of a detour monophonic graphoidal cover of $G$ is called the detour monophonic graphoidal covering number of $G$ and is denoted by $eta_{dm}(G)$. In this paper, we find the detour monophonic graphoidal covering number of corona product of wheel with some standard graphs