Monophonic and edge monophonic numbers of corona product graphs

<p>For a connected graph <span class="math inline">\(G=(V,E)\)</span> of order at least two, a <span class="math inline">\(u-v\)</span> chordless path in <span class="math inline">\(G\)</span> is a <span class="math inline">\(monophonic\)</span> <span class="math inline">\(path\)</span>. The <em>edge monophonic closed interval</em> <span class="math inline">\(I_{em}[u,v]\)</span> consists of all the edges lying on some <span class="math inline">\(u-v\)</span> monophonic path. For <span class="math inline">\(S'\subseteq V(G),\)</span> the set <span class="math inline">\(I_{em}[S']\)</span> is the union of all sets <span class="math inline">\(I_{em}[u,v]\)</span> for <span class="math inline">\(u,v\in S'.\)</span> A set <span class="math inline">\(S'\)</span> of vertices in <span class="math inline">\(G\)</span> is called an <span class="math inline">\(edge\)</span> <span class="math inline">\(monophonic\)</span> <span class="math inline">\(set\)</span> of <span class="math inline">\(G\)</span> if <span class="math inline">\(I_{em}[S']=E(G).\)</span> The <em>edge monophonic number <span class="math inline">\({m_1}(G)\)</span> of G</em> is the minimum cardinality of its edge monophonic sets of <span class="math inline">\(G\)</span>. In this paper the monophonic number and the edge monophonic number of corona product graphs are obtained. Exact values are determined for several classes of corona product graphs.</p>