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

Authors

1 Assistant Professor Department of Mathematics University College of Engineering Nagercoil Anna University, Tirunelveli Region Tamil Nadu, India.

2 Anna University, Tirunelveli Region Nagercoil - 629 004, India.

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

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